Originally Posted by
hvac1000
You might have a partially restricted orifice in the pilot burner. This can cause the problems you are having. Carefully remove the pilot assembly. Then carefully remove the aluminum tube from the assembly to gain access to the VERY small pilot orifice. Use a object smaller than the hole (very small single strand of stranded wire) to clean it and any other debris found there. Note: believe it or not very small spiders build a web in there which causes a problem in the area I live in.
Before you try to loosed the nut holding the aluminum tube spray with WD-40 and go easy. If not you might be buying new tube and nut assembly.
If this fails to fix it have a professional do an on site inspection to check the heat exchanger for cracks.