Why my "While wait() do" loop only works for once for really no reason?

You mentioned that it was a regular script in a Frame...

Before I share my answer I'll share with you an experience i had with doing the same thing:

When I click on a part, a gui (The frame) is supposed to pop up... however it pops up only ONCE. After I closed it, it never pops up again. I think the logic is the same behind this.

Therefore, I used RemoteEvents and put the script in a local script instead, and it worked perfectly fine after that. I have a way out here that (possibly) works

[[EDIT]]after the comments:

you mentioned that the real problem is really only about the Gui and the transparency not working.

that is because your old script was a Server-sided script inside a Frame. This cannot be used to change the transparency of the frame, as changing the transparency of a Frame would require a LocalScript. That's why we use the RemoteEvents to detect whether the oxygen breaking etc. changed

this is the server sided script in the workspace

local OxGenPlrDying = workspace.OxGenPlrDying
local OxGenIsOnAction = workspace.OxGenIsOnAction
local OxGenPlrHealing = workspace.OxGenPlrHealing --etc etc you get the idea
local RE = game:GetService("ReplicatedStorage").RemoteEvent
OxGenPlrDying:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenIsOnAction.Value,OxGenPlrHealing.Value)--add more parameters if you need!!!
OxGenIsOnAction:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenIsOnAction.Value,OxGenPlrHealing.Value)--add more parameters if you need!!!
OxGenPlrHealing:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenIsOnAction.Value,OxGenPlrHealing.Value)--add more parameters if you need!!!

--I think whenever each of the property changes you need to fire the local script to change the transparency
end)

The local script in the frame:

local function changeBackgroundTransparency(your_parameters)
    repeat
        
       wait(0.001)
    if game.Workspace.OxGenPlrDying.Value==true then -- remove every game.Workspace if you renamed your paremeter to OxGenPlrDying
        script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency-0.0001
        if game.Workspace.OxGenRestartComplete.Value==true then
            game.Workspace.OxGenPlrDying.Value=false
            game.Workspace.OxGenPlrHealing.Value=true
        end
    elseif game.Workspace.OxGenPlrHealing.Value==true then
        script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency+0.01 
        if script.Parent.BackgroundTransparency==1 then
            game.Workspace.OxGenPlrHealing.Value=false
        end
    end

    until script.Parent.BackgroundTransparency = 1 --i'm assuming you want it to be completely invisible. 
    

end

RE.OnClientEvent:Connect(function(your_parameters)
    changeBackgroundTransparency(your_parameters)
end)

So the logic here is that when oxygen level change, you fire the remote event which triggers the background transparency. it'll keep repeating the decrease/increase of background transparency until it gets the desired level.

i hope this was what you meant by your main problem

[ EDIT 2 ]

This is the first script, local script in the frame

local RE = game:GetService("ReplicatedStorage").RemoteEvent
local function changeBackgroundTransparency(OxGenPlrDying,OxGenRestartComplete)
    while wait(0.001) do
        if OxGenPlrDying==true then
            print("Player Dying")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency-0.0001
            if OxGenRestartComplete==true then
                OxGenPlrDying.Value=false
            end
        elseif OxGenPlrDying==false then
            print("Player Healing")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency+0.01 
            if script.Parent.BackgroundTransparency==1 then
            end
        end

end
    RE.OnClientEvent:Connect(function(OxGenPlrDying,OxGenRestartComplete)
--i changed the line below AND above, I removed the .Value from each. As well as everything above, I removed the .Value . I ' m actually not very sure whether it'll affect the script or not but from what I remember it'll cause an error if you have a `.` in your parameter
        changeBackgroundTransparency(OxGenPlrDying,OxGenRestartComplete)
    end)
end

Your second script should be fine.

For the third script, any particular reason to disable it? How are you going to enable it after disabling it?

[EDIT 3] The second script, I edited it a bit.

local OxGenPlrDying = workspace.OxGenPlrDying
local OxGenIsOnAction = workspace.OxGenIsOnAction
local OxGenRestartComplete = workspace.OxGenRestartComplete
local RE = game:GetService("ReplicatedStorage").RemoteEvent

OxGenPlrDying:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenRestartComplete.Value)
end)

OxGenRestartComplete:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenRestartComplete.Value)
end)

--and if you need;

OxGenIsOnAction:GetPropertyChangedSignal("Value"):Connect(function()
    RE:FireAllClients(OxGenPlrDying.Value,OxGenRestartComplete.Value) --you may have to add a OxGenIsOnAction parameter 
end)

[EDIT 4] I edited your first script a little more. I reckon the problem should be in here since it didn't print out what's necessary.

local RE = game:GetService("ReplicatedStorage").RemoteEvent

RE.OnClientEvent:Connect(function(OxGenPlrDying,OxGenRestartComplete)
    while wait(0.001) do
        if OxGenPlrDying==true then
            print("Player Dying")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency-0.0001
            if OxGenRestartComplete==true then
                OxGenPlrDying.Value=false
            end
            elseif OxGenPlrDying==false then
                print("Player Healing")
               
 script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency+0.01 
            if script.Parent.BackgroundTransparency==0 or script.Parent.BackgroundTransparency==1 then break
            end
        end
    end
end)
--I may have missed out an "end" somewhere but most likely not

[EDIT 5]

I further edited your first script. Hopefully this works a bit better. Also sorry for the really late reply, was quite busy

local RE = game:GetService("ReplicatedStorage").RemoteEvent

RE.OnClientEvent:Connect(function(OxGenPlrDying,OxGenRestartComplete)
    while wait(0.001) do
        if OxGenPlrDying==true then
            print("Player Dying")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency-0.0001
            if OxGenRestartComplete==true then
                OxGenPlrDying.Value=false
            end
        elseif OxGenPlrDying==false then
            print("Player Healing")
        end
        script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency+0.01 
        if script.Parent.BackgroundTransparency==0 or script.Parent.BackgroundTransparency==1 then break
        end
    end
end)

[EDIT 6] Well this seems pretty challenging to me. None of the above solutions really worked... no really sure if this will now. To be honest i don't know why Player Dying and Player Healing keep printing... the only reason for that is that the BoolValue keeps alternating between false and true. At this point, really the only way is to keep trying different methods of writing your script add a remotefunction called "RemoteFunction" to your replicated storage and try this!

your first script (local script): warning this may cause lag but hopefully it doesn't

local RE = game:GetService("ReplicatedStorage").RemoteEvent
local RF = game:GetService("ReplicatedStorage").RemoteFunction

RE.OnClientEvent:Connect(function(OxGenPlrDying)

    while wait(0.001) do
        if OxGenPlrDying==true then
            print("Player Dying")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency-0.0001
            if workspace.OxGenRestartComplete.Value == true then
                RF:InvokeServer()
            end
            
        elseif OxGenPlrDying==false then
            print("Player Healing")
            script.Parent.BackgroundTransparency=script.Parent.BackgroundTransparency+0.01 
        end
        if script.Parent.BackgroundTransparency==0 or script.Parent.BackgroundTransparency==1 then break
        end
    end
end)

in another new script [Script 4] a Server-Sided-Script in Server-Script-Service:::::::

local RF = game:GetService("ReplicatedStorage").RemoteFunction
RF.OnServerInvoke = function()
    workspace.OxGenPlrDying.Value = false
end

i'm actually quite confident that this will work now lol, if it still doesn't that would be quite sad xD.

i deleted the first draft because when i tried to edit it said : "Whoa there! That's some awful long text. Please stay below 10,000 characters!

"