Q: Battery dies when car parked

Battery becomes very weak after being parked more than approximately 4 hours. Can still start after 3 - 10 tries, usually closer to 3 - 4 tries, if sits up to 24 hrs. After that highly questionable if will start. If sits a couple of days will not start - battery dead. Removing cable connection and then reconnecting just before drive helps, but not entirely. Will most often start but takes a number of tries. If don't drive for 2 or 3 days will not start if cable connected and may not start if cable not connected. Possibly connected to fuel pump or something else to do with the fuel. Have noticed it starting better when tank is full or not sure but if use better quality gas. Have not been able to find any obvious drains on battery like a light staying on. If drive a couple of miles, battery will hold charge for a good two plus hrs. No problem starting. Any longer battery begins to weaken. Also, car had continued to run after removing key. Think this has stopped since using better gas.

My car has 180000 miles.
My car has an automatic transmission.