(This tip provided by John Ghidiu)
Sometimes evolution will be out of sync with the exchange server. As I write this it’s a known problem. The workaround is to force evolution to shutdown and then force it to rebuild the local folder cache.
It seems that Evolution getting out of sync with Exchange is an old, old bug. If you run:
rm -rf ~/.evolution/exchange//folders.db (this is the cache, I think)
and then start Evolution again, things work again.