Until is used when we want to indicate that something can or will change after a period of time or when something evolves after a period of time
I will watch television until 5PM
Keep stirring until the mixture is smooth
Unless is used to indicate that something can or cannot currently occur, but that this could be inversed if some condition is met.
I will go cycling tomorrow unless it rains
You can’t get in unless you’re on the list
In your example it is clearly a period of time which is in play, so only until fits.