Why would furnace pilot light go out?

check and make sure it is clean.

after enough time a white powder residue builds up from burning the gas.

sometimes this powder will plug an opening slightly just enough to put it out but not keep it plugged. while you're in there clean the powder off the thermocouple too, too much on it and it will actually insulate it against the heat, thermo will be too cool and not allow gas to come thru.

Hi,

Could be a draft, also they will go out if the gas box becomes faulty & will automatically disable the pilot to avoid serious problems. If it was able to re light & the burner goes on with no problems than you should be fine. One thing to consider is the thermo-coupler might be failing, always a good idea to keep a spare on hand as they tend to fail on the coldest night.

Wind blowing through the structure where the pilot light is located. or Temporary interruption of gas supply.

One of two things the wind is coming though the chimney or the thermo coupling is going bad.