How could I fix this?

Your main problem was because repeat didn't have a wait. Repeat is a loop, if it doesn't have a wait, like a while statement, it will crash or force a break request to happen in studio.

local RoundLength = 10 -- How long the rounds are in seconds.
local IntermissionLength = 5 -- How long the intermission is in seconds.
local RoundStartTime -- To tell when the round starts.

-- Use WaitForChild() on children
-- Why not just put this in ServerStorage off the bat?
local map = workspace:WaitForChild("Map")
map.Parent = game:GetService("ServerStorage")


local function initialize()
    local MapCopy = map:Clone()-- A copy of the map
    MapCopy.Name = "MapCopy"
    MapCopy.Parent = game.Workspace
    RoundStartTime = tick() -- Tick = What current time is in seconds.
	-- returns your cloned map so we can use it later, rather than trying to 
	-- find it again
	return MapCopy
end

local function cleanup(this_map)
    this_map:Destroy()
end

while true do
    local this_map = initialize()-- Puts current time in round start time.
	-- repeat is a loop, so it needs a wait
	repeat  wait()
	    local CurrentTime = tick()
	    local TimeSinceGameStarted = CurrentTime - RoundStartTime
		print(TimeSinceGameStarted)
	until TimeSinceGameStarted > RoundLength
	    cleanup(this_map)   
	wait(IntermissionLength)

end