How to stop pilot on gas hot water heater from going out ? I even cleaned the filter but this did not help. Pilot stays light for about 15 minutes then goes out.

You have a bad thermocouple or dirty flame rod. See which one you have. The flame rod can be cleaned with 1000 grit sandpaper; if it has a thermocouple you must replace it with a universal kit available at any hardware store. Make sure only 3/8" of tip has flame on it.