Hello everyone!

I am puzzled with the following problem: 

my car cranks but doesn’t start if you don’t give it a few hours break before you try to start it again.

more details: when I use the car for commuting (morning and evening every day) it works, no problems. But when I decide to go shopping or play tennis, and try to start it after it only had an hour or two of break, it just won’t start. I got used to this issue, so I now try to do my shopping trips as drive ups on my way back from work so I don’t have to stop the car. When I happen to get stuck somewhere, I would just find alternative transportation, and come back to it the next morning, and it would start with no issues. But that’s annoying! I went to Autozone to check on battery/starter/alternator, they said I had a weak battery which was the problem. I replaced the battery, but the issues only worsened over time. Please let me know if any more details needed.

Car: Chevrolet Malibu 2003, 293k miles, automatic.

Thank you!