Yes, the CR2032 battery will age and eventually go short circuit, loading down the charging circuit, which will load down the +5 volt rail and cause the 3000 to crash.
I replace the batteries with a set of flying leads, and attach those to a CR2032 battery holder, so future battery changes are easy - no more soldering! Some good quality double sided tape then completes the job holding the battery holder in place.
I do wonder why AOR didn't design their radios in this way the first time. Receivers of this quality will definitely outlast the shelf life of a CR2032 cell.