The pilot light sometimes does not light and sometimes when it does the burner doesn't light or even goes out once lit. Does anyone know what the problem is?

Sound similar to the problem I ran into recently with an AO Smith hot water heater. The new ones come with a closed chamber. The air supply is through a ceramic filter under the main burner and pilot. If the ceramic filter is clogged or dirty, the pilot and burner will shut off.

On the other hand, it could be as simple as a thermal coupler that has gone bad and needs replacement. Good Luck...