Bob, if you can sucessfully get the pilot to operate on it's own BEFORE the main burner comes on, then the thermocouple is working properly and we can go to the next step.
It sounds like you may have a weak or dirty pilot. Check to see if your pilot flame burns in a nice, steady blue flame, or does it flicker and burn somewhat yellow? If it's not almost totally blue and seem to burn steady you may need to clean the pilot flame orifice and be sure it is unobstructed.
It is also possible, but less likely, that there is an obstruction in the gas line from the valve to the pilot, or that the pilot valve itself is failing.
Naturally, for safety reasons, I would advise caution in attempting any repairs you might not be comfortable with.