Can somebody explain to me why the second repeat doesn't work?

This is because of conditional loops. Currently, the first loop is a wall for any code written prior to that loop. It has to break in order for newer code to run. A fix would be to use the spawn function, or just use a for loop!. And you don't have to manually set the text each time, use string.sub!

local welcome = "Welcome"

local k = script.Parent
local s = script.Parent:FindFirstChild("Click")
local hm = script.Parent:FindFirstChild("vhs thing")
local other = script.Parent:FindFirstChild("Sound")
hm:Play()
wait(0.5)

for i = 1, welcome:len() do
    wait(0.1)
    k.Text = welcome:sub(1, i) -- cool function that gives text typewriter effect
end

wait(1)

for i = 0.1, 1, 0.1 do -- loop the transparency 
    wait(0.1) 
    k.TextTransparency = i
end

wait(3)

for i = other.Volume, 0, -0.1 do -- loop at the volume to 0
    wait(0.1) 
    other.Volume = i

    if i <= 0 then -- if i is 0 destroy script.Parent
        script.Parent:Destroy()
        break 
    end
end

The second loop could be

while true do
    other.Volume = other.Volume - 0.1
    wait(.1)
    if other.Volume == 0 then
        script.Parent:Destroy()
    end
end)