Not really, since I haven't flown them much. I was denied boarding once when I presented myself to the agent 21 minutes before flight time (flight was at 9:10; despite getting lost on the way to the airport, then getting stuck in traffic, and having to navigate Midway's "new improved" parking, I presented myself to the agent at 8:49 per the airport digital clocks; this was well before 9/11 btw). I ended up getting a walk-up fare on Southwest.
Still, the three flights I've had on ATA seemed okay. Nothing exceptional, but other than the missed flight I don't recall any problems.
More or less the same thing happened to my daughter, when she lost track of time while waiting for her connection. Still she was at the gate before the "no show" time.
I missed a connection from Boston via Atlanta to Dallas, the delay in Boston wasn't their fault, nor was it weather. Their tickets are not good on other airlines, and mine were non-refundable. So I was stuck either paying for something I'd never use, or waiting until the next flight. I chose waiting, although that made me miss my connection on American to San Antonio, and they also would not refund or honor the ticket for the next morning's flight. So I took Southwest from Dallas, as it's walk up fare was considerably less than it would have cost to "re-book" the American ticket. Fortunately I had a place to stay in the DFW area without also getting stuck for Taxi and hotel. It did cost me another day of vacation time though, when I was only getting two weeks per year, after being Clintonsized out of my 20+ years senority with 4 weeks of vaction per year job.