1992 Acura Vigor run fine in the mornings

I have a 1992 Automatic Acura Vigor with around 138,000 miles on it that has issues starting. Typically it will start and run fine in the mornings and the evenings but not so much during the day. However it will go through spurts of starting for a few days then one day it will switch and will not start. When it doesn't start it will typically have to sit there for a few hours before starting again. I have taken the car to three mechanics and they cannot solve the problem. They have checked the car on the computer and nothing. What could possibly be the problem as I typically leave the car on instead of turning it off to go into a store? Also, the area where the muffler is connected has rusted through so what is the expected cost of having this repaired? Please keep in mind my knowledge of cars is very limited. Thanks