kmail and akonadi repeatedly ask (at intervals of 10-60mins, so not a problem) for password to open KDE wallet on behalf of one of the IMAP resources (same one every time). But kmail never manages to actually fetch any mail from that IMAP resource. I think this might be related to "[Bug 323287] Kmail doesn't send email, Mail Dispatcher Agent doesn't work" in that the cited behaviour only happens when I also see the "cannot fetch mail that we know exists in gmail folder" behaviour described in that other bug. Reproducible: Always Steps to Reproduce: don't really know what causes this behaviour.
It turns out, this bug was being caused by a corruption of the kde wallet. I recreated the wallet and have been working happily for a couple of weeks; then today something caused the wallet to be corrupted again, and I can no longer access my IMAP mail resources.