Gas and Oil Home Heating Furnaces - Pilot light won't stay lit

I'm a first time home owner and only been here a few months, so please forgive any stupid questions I might ask.

We ran into this problem last night when we couldn't get any hot air from the furnace. I checked it out and noticed the pilot light wasn't lit. I re-lit it and got the hot air flowing again. However, once our house got to the thermostat temperature, that's all we got! I had to get up there and re light it this afternoon to get more hot air going.

So what could be causing our pilot light to keep going out? And by the way, it's a gas furnace if that helps.

Thanks!

Probably just needs a new thermocouple...