I just bought a used Sony CDP-M555ES. It skips occasionally during play. Is it worth repairing? Is it something I could do myself?
Call Sony, they will repair for a flat fee.
Have mine hooked to a DAC by PS audio. It sounds great and makes changing CDs a breeze as you already know. Downside it only as a toslink output.
If it is occasional then it may be your discs (did you have them laying around like most people - taking in and out of jewel cases and dropping them is how they get scratched) or it may need to be placed in a quieter environment - the changers are very susceptible to skipping when bumped. (On a stand on a wobbly floor if you jump then you can expect it to skip)

A new Sony 300 disc megachanger is around $200 on ebay- - so hardly worth repairing - just hook it up to a good DAC with excellent jitter rejection and off you go... no need to get the ES models with the slightly better DAC...(which are all like 10 years old now anyway and mechanically may not have more than five years left in them)

I have five changers and have not had one fail in 12 years of use. Great if you have a large collection and actually want to hear it and you want to protect your discs from dust and damage from handling. (I use software to control them all)

A word of caution if you move the changer (from one room to another etc.) then some CD's can easily tip out of the tray and it is quite possible to damage many of them when the player tries to rotate the tray and access them - if you hear clunky noises that indicate that it is jammed then unplug immediately and remove the cover (philips screws) and carefully put back the CD's and cover before plugging it back in.

I hope this helps....
BTW - You can repair CD's with a $20 device from any Gaming shop - polish the surface to remove scratches.
I've had skipping in both of my Sony's only when the discs were dirty, so you might check for scratches/dirt. FWIW, you should always use CDRs, which the Sony's will recognize, rather than your original discs, as the Sony's are notorious for scratching discs.