Gas-fired hot water heater safety question - pilot flame will not stay lit. How long can I wait to fix?

My hot water heater works, but whenever it is done heating it shuts off and the pilot does not stay lit. Which means every time we need hot water, I need to either use what's left in the heater or fire the whole thing up again (light pilot, wait for it to stabilize, then turn the unit on). I believe somehow when the main flame goes off after heating it somehow extinguishes the pilot too. I have to wait 2 more weeks to get this fixed for free - what should I do?