From the sound of it some kind of safety has kicked in. There's probably a thermocouple that's connected to a cut off valve of some sort. If the gas is on, but the thermocouple is too cold, it cuts off the gas (this is intended to prevent something blowing out the flame from filling your home with gas!).

Look around and see if you can spot the thermocouple and make sure it's not bent out of the way or something silly like that. Beyond that, I'd call for service on the thing.

Here are a few things to consider, from a Reliance water heater Installation Instructions and Use & Care Guide.

Safety Shut-off
This water heater is designed to automatically shut-off in the event of the following:

1. The pilot flame is extinguished for any reason.
2. The water temperature exceeds 195°F (91°C).
3. Excessive build up of dust on the base ring filter or flame arrestor. See Maintenance of your Water Heater Section.
4. The ignition of flammable vapors.

A thermocouple is used to determine if a pilot flame is present, and will shut off the gas supply to the main burner and the pilot if the flame is absent. This unit is also equipped with a thermal switch, designed to shut off the gas supply in the event the water heater has been exposed to flammable vapors (e.g., spilled gasoline), poor combustion caused by a blocked vent or insufficient combustion air. If the thermal switch opens:

1. Check the flame-arrestor for signs of high temperature (blue or black discoloration). See Figure 29.

   
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2. If there are signs of high temperature, inspect your installation for any problems with venting, combustion air supply and for a flammable vapor event (see "Pilot Light Troubleshooting Flow Chart" section). Correct any issues prior to resetting the thermal switch. If you suspect a flammable vapor incident has occurred, do not use this appliance. Immediately call a qualified technician to inspect the appliance. Water heaters subjected to a flammable vapors ignition will require replacement of the entire water heater.

3. Reset the thermal switch by depressing the small button in the center of the thermal switch. Follow the Lighting Instructions found on the front of your water heater

A high temperature limit switch or ECO (Energy Cut Off) in the tank is used to shut off the unit if the water temperature exceeds 195°F (91°C). The ECO is a single-use switch, which, if activated, requires complete replacement of the entire gas control valve/thermostat. If the ECO should activate, the water heater cannot be used until the gas control valve/thermostat is replaced by a qualified technician. Contact your local dealer for service information.

Also make sure you check and clean the base-ring filter.

External Inspection & Cleaning of the Base-Ring Filter

1. At least annually check the base-ring filter (Figure 29) for any dust or debris that may have accumulated on the filter screen. NOTE: If the water heater is located in an area that is subjected to lint and dirt, it may be necessary to check the base-ring filter more frequently.
2. Follow the Lighting Instructions to turn off the water heater and allow it to cool for 10 minutes before attempting to clean the base-ring filter.
3. Use a vacuum cleaner with a hose attachment to remove any dust or debris that may have accumulated on the filter. NOTE: If unable to inspect or clean the base-ring filter, follow the “Cleaning the Combustion Chamber and Flame-arrestor” instructions.
4. After the base-ring filter has been cleaned, follow the Lighting Instructions to return the water heater to service.

The guide also has a pretty good troubleshooting section.

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Make sure the unit has plenty of combustion air. Often after a flood in the basement, folks tend to shuffle things around. If things are stacked too closely to the appliances, the combustion air to appliances can be restricted.