Round-based timer not counting backwards?

I think I know your problem: you are using the startergui instead of the players playergui.

The playergui is what the player currently sees and the startergui is what appears when you spawn in/join the game.

To do this you will need to set a variable for the player gui like this:

local player = game.Players.LocalPlayer
local plrGui = player.PlayerGui

Now that we have that we will need to change your code:

local player = game.Players.LocalPlayer
local plrGui = player.PlayerGui
local intermissionTime = 30 -- in secs
local roundTime = 180 -- roundtime in secs
local timerMode = 1 -- 1 means intermission, 2 means round mode

local timerGui = plrGui.timerGUI

while wait(1) do
    -- set timeLabel text to whatever the time left is
    if timerMode == 1 then
        roundTime = 180 -- set roundTime back to 180 since we're
                        -- in intermission right now
        intermissionTime = intermissionTime - 1
        timerGui.Frame.timeLabel.Text = (tostring(intermissionTime))

        if intermissionTime < 1 then
            timerMode = 2
        end

    elseif timerMode == 2 then
        intermissionTime = 30 -- set intermissionTime back to 30

        roundTime = roundTime - 1
        timerGui.Frame.timeLabel.Text = tostring(roundTime)

        if roundTime < 1 then
            timerMode = 1
        end

    end
end

Also you need to use a local script if you are not already.

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