Why will this only work once?

It's because a song is moderated or that you try to use the script from a LocalScript, Here you have a handy code that can run on the LocalPlayer and on the Server (Workspace, ServerScriptService etc.)

--Config--

local isLocalPlayer=true
local SoundIds = {
'http://www.roblox.com/asset/?id=243372213',
'http://www.roblox.com/asset/?id=319758951',
'http://www.roblox.com/asset/?id=236896548',
'http://www.roblox.com/asset/?id=181547615',
--'http://www.roblox.com/asset/?id=283801001', --This song is moderated which means it cannot be played.
'http://www.roblox.com/asset/?id=306412637',
}

--End of Config--

-- isLocalPlayer will only work in a LocalScript!
-- Place a LocalScript in StarterGui if you want to use isLocalPlayer and make sure the setting it's enabled too :) Oh and don't forget to paste this code into it too :)

local Music

if script:IsA("Script") and not script:IsA("LocalScript") then isLocalPlayer=false end --Some precaution :)

if isLocalPlayer then
Music = Instance.new("Sound",game:GetService("Players").LocalPlayer)
else
Music = Instance.new("Sound",game:GetService("Workspace"))
end
-- I recommend using GetService instead of just game.Players or game.Workspace since if they're renamed, the script will break.

while true do --insert and play sound
Music.SoundId = SoundIds[math.random(1, #SoundIds)]
Music.Volume = 1
wait(1)
Music:Play()
Music.Ended:wait() -- Waits for the music to end to play the next music audio
wait(1)
Music:Stop()
end