No, there are no electric solenoid valves in the LP system. The 'push to start' button opens air to the pilot light. That your's shuts off indicates it is not getting it's operating air supply, no doubt a flue problem. Remember, this is a two-way flue supplying air and exhausting heat at the same time. See the flue bulletin posted on the Tech Drawings link. It may look good but have lost it's seal or have an out-of-sight blockage that the 'push-to-start' is just bypassing.