I re-read the OP, and now see that they aren't the original rings. That convinces me that it's either an issue of separation or phasing (or both).

Check the separation carefully by placing your chain against the inner face of the outer ring and seeing if the plates touch the tops of the inner ring's teeth. They shouldn't, the chain should be forced over so the inner plate is just outboard of the tip if the inner ring's teeth. Otherwise it'll ride the teeth rather than dropping in cleanly.

It could be that this was OK for a while, but with some tooth wear the problem worsened. If both rings are Campy brand, it's possible hat you have a 9s ring on the outside rather than a 10s. Or if it is a 10s, it's of a later vintage, and lacks the relieved (I don't know if they changed since 2004) area on the inner side of the mounting area. This was intended to move the ring inboard on 9s and earlier cranks (used on OEM 10s until 2004 at least).

Either way, if you see a chainring gap issue as described, fixing it (by any means) will solve the problem.