Toqwik

I have a 91 305 tbi convertible. It has not left the garage in a year but I start it every week and it has stabilizer and fresh octane boost. It runs perfect for about 10 minutes. When it quits sometimes it stumbles sometimes it quits like the keys was turned off. Sometimes when it stumbles and dies it sounds like a short that I assume is the injectors trying to fire. I have even tried putting a screwdriver between the tbi and the linkage to keep the idle high and no help. I can the new try to restart and it won't start. I can let it sit 15 minutes and it fires right up and runs perfect again. This car is 100% original has all the pollution control and the cat is still there. I have replaced the ignition module but no change. This was my daily driver a few years ago and have never had an issue. I'm stumped, what are your thoughts? Thanks in advance.
Scott.