Primarily, this can be caused by two things:

1. your chain being too loose. research proper fixed gear chain tension and do it.
2. your chainline being way off. The less straight your chain is, the more likely it is to come off. If your chainline is off by a lot, you'll probably need to get new components if you want to fix it. One thing you can possibly do is move your chainring from the inside to the outside of the crank arm or the other way around. You can research more about this if you suspect a misaligned chain.