The pilot light jet may have got a little bit of dirt or grit in it which is preventing it from keeping alight. Try probing the jet with a fine piece of wire to see it the blockage can be dislodged. You may have to unscrew the jet to clear it by blowing air through it. Make sure gas is turned off first before removing any parts.

The pilot light also has a thermocouple that allows gas to the pilot light while the flame is burning. If flame goes out it shuts gas off to the pilot jet. The thermocouple is bypassed by a switch during the initial ignition and once the thermocouple warms up after a minute or two of holding in the bypass switch, it should maintain the pilot. If, after cleaning, the pilot light keeps going out, it would seem that your thermocouple is faulty and needs to be replaced