I have a Tempstar natural gas furnace. It has electric element for
ignition of the pilot.

It was working fine all December. Now, it does not work as follows:
the draft fan starts and runs correctly, then a good looking pilot
light comes up. In less than one second, the pilot light turns off and
the main burner does not ignite.

I spent a while troubleshooting this issue. I cleaned the pilot sensor
with light emery cloth. It did not seem to help. It seems that if I
remove two screws holding the pilot light in place and pull it out of
the furnace, it does ignite and hold, and if I insert it back into the
furnace, the main gas ignites.

I put it back in and everything seems to work. I turn the furnace off,
then on, and the pilot stays and the burner lights. Then I went to
sleep and again woke up in a cold house.

Overall this behavior seems to be somehow "erratic". As in, things
seem to work, then after a while the pilot starts going away again.

Would there be some coherent explanation of this behavior.