I have a question about my home gas water heater.The gas water heater pilot lit can not keep on when I release the gas control knob.

Replacing the thermocouple is easy and fairly cheap, sounds like your issue. https://www.google.com/?gws_rd=ssl#q...r+thermocouple

You can test it first*, Hot Water Heater Pilot Light Won't Stay Lit or On - How to fix waterheater by testing Thermocouple


https://www.youtube.com/watch?v=S3Xnek1s6Us

*3rd video in above link.