I'm presuming this is for an imap mail account. Do you only download headers or have you set it up to keep copies of full emails ? Have you synchronised the folder for offline use to get full copies of emails downloaded into the Inbox? Do you have an Anti-Virus product scanning incoming mail? If yes, then access AV and switch off email scanning.

I keep full copies in TB and also synchronise folders when I go into offline mode. I get copies of some emails put into Local folders, but I do it in offline mode, so the folder does not attempt to synchronise whilst I'm doing it.