GE water heaters have some of the worst water heater reviews on the internet. Some of the most common issues with GE is related to the gas valve. In some cases replacing the thermocouple has resolved the problem or at least temporarily.
The pilot light tends to self extinguish which can either be the thermocouple or gas valve. If the gas valve is bad it may not be worth replacing, especially if the tank is out of warranty. The labor on a GE water heater is only covered for 1 year, so any troubleshooting or time invested in parts will not be covered.
If you decide to try and repair a GE water heater that the pilot is not working on you can contact GE customer support at 1-800-431-1549. The first thing they will try is to send out a new thermocouple, pilot gas line, piezo electric line, and gasket kit. You should be able to get them to overnight you the parts. Start with this before calling out a plumber to avoid an extra trip charge.
Once you have the parts you can contact us to try and replace the parts or you can try it yourself by watching this DIY video on replacing a thermocouple.
For many homeowners, this has not solved the problem and the gas valve is usually the next item they will try to send out. Many people have been able to just get a new unit by bringing the old defective unit back to the store. You will still have to pay for labor and materials on the new installation but at least you will have hot water, until it fails again anyway.