How could I make this script work when a player respawns rather than joins the game?

Loop through the players at the start of the script, so re-adding it won't will still work.

local function characterAdded(Ch)
        local g = script.Arm1:clone()
        g.Parent = Ch
        local C = g:GetChildren()

        for i=1, #C do

            if C[i].className == "Part" then
                local W = Instance.new("Weld")
                W.Part0 = g.Middle
                W.Part1 = C[i]
                local CJ = CFrame.new(g.Middle.Position)
                local C0 = g.Middle.CFrame:inverse()*CJ
                local C1 = C[i].CFrame:inverse()*CJ
                W.C0 = C0
                W.C1 = C1
                W.Parent = g.Middle
            end

            local Y = Instance.new("Weld")
        Y.Part0 = Ch["Left Arm"]
        Y.Part1 = g.Middle
        Y.C0 = CFrame.new(0, 0.4, 0)
        Y.Parent = Y.Part0

    end

    local h = g:GetChildren()
    for i = 1, # h do
        if h[i].className == "Part" then
            h[i].Anchored = false
            h[i].CanCollide = false
        end
    end
end

for _,plr in next, game.Players:GetChildren() do
    plr.CharacterAdded:Connect(characterAdded)
end

game.Players.PlayerAdded:connect(function(player)
    player.CharacterAdded:Connect(characterAdded)
end)

NOTE: You should probably not delete the script and re-add it.

So if you are adding the script after deleting it, the reason why your script isn't working makes sense.

For the CharacterAdded event to work, you must get a Player first. When your script is first ran, the Player is obtained through the PlayerAdded event, but once that script is deleted and added again, the PlayerAdded event is not ran because the Player is already in the game, which will result in the code not being ran.

My only suggestion is to find a way to run this script without deleting it every time.