Is there a way to make this run more than once without a while loop?

This works, but only once, I need it to work when either of the events are fired, but I've tried multiple ways and none of them work.

Code:

local fram = script.Parent.back
local plr = script.Parent.Parent.Parent
function UpdateOldLabels(Parent)	
	for i,v in pairs(Parent:GetChildren()) do
		if v.Name:sub(1,4):lower() == "item" then
			local LineNumber = v.Name:sub(5)
			v.Name = "item"..tostring(tonumber(LineNumber) + 1)
			v.Position = v.Position + UDim2.new(0.02,0,0,0)
		end
	end
end

if game.Players.PlayerAdded or plr.Inventory.ChildAdded then
	for _,v in pairs(plr:WaitForChild("Inventory"):GetChildren()) do
		local item = Instance.new("ImageButton", fram)
		item.BackgroundTransparency = 1
		item.Name = "item1"
		item.Size = UDim2.new(.02, 0, .6, 0)
		item.Position = UDim2.new(-.02, 0, 0.15, 0)
		item.Image = "rbxassetid://"..tostring(v.itemPrev.Value)
		item.ZIndex = 2
		UpdateOldLabels(fram)
	end
end

Make a function for them both, then make separate connection lines;

local fram = script.Parent.back
local plr = script.Parent.Parent.Parent

function UpdateOldLabels(Parent)    
	for i,v in pairs(Parent:GetChildren()) do
		if v.Name:sub(1,4):lower() == "item" then
			local LineNumber = v.Name:sub(5)
			v.Name = "item"..tostring(tonumber(LineNumber) + 1)
			v.Position = v.Position + UDim2.new(0.02,0,0,0)
		end
	end
end

--function for both
function doit()
	for _,v in next,fram:GetChildren() do 
		v:Destroy() 
	end
	for _,v in pairs(plr:WaitForChild("Inventory"):GetChildren()) do
		local item = Instance.new("ImageButton", fram)
		item.BackgroundTransparency = 1
		item.Name = "item1"
		item.Size = UDim2.new(.02, 0, .6, 0)
		item.Position = UDim2.new(-.02, 0, 0.15, 0)
		item.Image = "rbxassetid://"..tostring(v.itemPrev.Value)
		item.ZIndex = 2
		UpdateOldLabels(fram)
	end
end

--separate connection lines
game.Players.PlayerAdded:connect(doit)
plr.Inventory.ChildAdded:connect(doit)