Mike
You commented: "So at this point it should only be merges requested from the tree, before last October or so, that don't always complete when you approve them. If that doesn't seem to match your experience, reply here with whatever detail you can, and I'll investigate."
That does not match my experience, and I believe the reason is because of multiple managers. Let's suppose there are two profiles, one with 100 managers, and the other with 1 manager. Assume the 1 manager doesn't have collaborators; maybe his profile is private; and he didn't initiate the merge.
All 100 managers of the first profile will see the merge in their merge centre, and all 100 managers can approve the merge as much as they like but they won't be able to complete the merge. In these very common multiple manager cases, merges do not always complete when you merge them.
It's also possible for a merge to be initiated by someone who isn't a manager or collaborator on either side, in which case two approvals will also be likely to be required.