Why does this stop after working twenty-one times?

I modified your script a little to display the name and property each time the Changed event occurs so you know exactly what is changing.

repeat wait() until Workspace:FindFirstChild(Game.Players.LocalPlayer.Name)
local p=Instance.new("Part")
p.Transparency=1
p.Size=Vector3.new(2, 2, 2)
p.CanCollide=false print(3)
p.Parent=Game.Players.LocalPlayer.Character
local mouse=Game.Players.LocalPlayer:GetMouse()
local b = Instance.new('BodyGyro')
b.maxTorque = Vector3.new(math.huge, math.huge, math.huge) print(7)
b.cframe = mouse.hit
b.Parent = p
local active=false
i=1
function fix(part, property)
    print(i, part, property)
    i=i+1
    if active==false then
        active=true
        p.CFrame=Game.Players.LocalPlayer.Character.Head.CFrame
        p.CFrame=CFrame.Angles(0, math.rad(p.Rotation.Y), 0)
        b.cframe=mouse.hit
        active=false
    end
end
p.Changed:connect(function(prop) fix("p", prop) end)
Game.Players.LocalPlayer.Character.Head.Changed:connect(function(prop) fix("Head", prop) end)
mouse.Changed:connect(function(prop) fix("mouse", prop) end)

Following is the output:

3

7

1 Head BrickColor

2 p CFrame

3 p Position

4 p Rotation

5 p CFrame

6 p Position

7 p Rotation

8 Head Color

9 p CFrame

10 p Position

11 p Rotation

12 p CFrame

13 p Position

14 p Rotation

15 p Parent

16 p CFrame

17 p Position

18 p Rotation

19 p CFrame

20 p Position

21 p Rotation

From this you can see that the CFrame and Position of the part continue to change as the part falls out of the world. Once the part is destroyed by falling too far, it stops receiving Changed event calls and so it stops writing to the console.

It seems you are not expecting this part to fall to its doom but that is what is happening.

Your debounce doesn't really work properly as there is no waiting before "deactivating", which basically renders it useless.

That's what I think causes the problem. Give it a try:

repeat wait() until Game.Players.LocalPlayer.Character
local p = Instance.new("Part", game.Players.LocalPlayer.Character)
p.Transparency = 1
p.Size = Vector3.new(2, 2, 2)
p.CanCollide = false
print(3)

local mouse = Game.Players.LocalPlayer:GetMouse()
local b = Instance.new('BodyGyro', p)
b.maxTorque = Vector3.new(math.huge, math.huge, math.huge) 
print(7)
b.cframe = mouse.hit
local active = false
local i = 1

function fix()
    print(i)
    if active == false then
        i = i + 1
        active = true
        p.CFrame = Game.Players.LocalPlayer.Character.Head.CFrame
        p.CFrame = CFrame.Angles(0, math.rad(p.Rotation.Y), 0)
        b.cframe = mouse.hit
        wait(0.1)
        active = false
    end
end

p.Changed:connect(fix)
Game.Players.LocalPlayer.Character.Head.Changed:connect(fix)
mouse.Changed:connect(fix)