My pilot light will light, but will not stay lit? I have a gas whirpool water heater aprox 1 1/2 years old.Thisis the first time we have encountered any problems with our appliance.

Once the flame has struck it heats up a thermocouple that in turn holds the gas valve open

It is a safety measure in case the flame blows out and the gas keeps on coming.

Sometimes the end of the thermocouple gets dirty and a scrub with a fine emery board does the trick

If not it is a new part (They are not that expensive)

The pilot light needs to heat up the thermocouple, the heat from the pilot light lets the gas valve know that the pilot light is lit and the appliance is ready and that it is safe to leave gas flowing to the pilot after you release the pilot light button. Sometimes soot gets built up on the thermocouple and doesn't allow it to heat up like it needs to and won't send the signal to the valve that the pilot is lit and when you release the light pilot button on the valve, the gas get's cut off and the pilot goes out. One of the first things you would want to try before replacing the thermocouple is to clean it. But before you go to any trouble... are you leaving the button on the gas valve pressed for at least 30-45 seconds after lighting the pilot?
If you are giving the pilot a reasonable amount of time to heat the thermocouple, it might just need to be cleaned vs. replaced.
Some fine steel wool or sos pad is usually enough to clean off the thermocouple. After cleaning it, make sure that it is making good contact with the pilot light to get it to heat up properly (about a half inch of the tip should be in the flame)
If cleaning doesn't work, you may have to replace the thermocouple with a new one.
Hope that works for you.