Just to throw in my 2cents worth, I've had a Pioneer 300-disc jukebox for a couple of years now, and it works flawlessly. I also have two Denon single-disc universal players. The reason I have the CD-only player is the feature that none of the universal players have: shuffle play. The Pioneer (and Sony) also let you compile playlists from the installed discs, which is a feature I use frequently.
The skipping problem you're experiencing is undoubtedly caused by the transport circuitry/mechanics failing as the unit heats up. It's probably not cost-effective to have this thing repaired, as a new player would probably be about the same price.
To go a step further, as others here have mentioned, a media server is probably the smartest thing to move to these days. I considered those when I bought my jukebox, but they were just too expensive at the time. Prices have plummeted since then, so you might just consider moving away from mechanical CD players altogether. That's what I'm going to do next.