I have got some users and myself experienced this. We are on BES for Domino. Users are randomly receiving old mail from anytime a year to a few months back.
The administrator has not been able to explain why it happens.
However, we noticed that if we did a hard reset, the old mail just get removed from the device since they longer exist in the mailbox.
If anybody can explain why, it'll be 1 less headache for the BESadmin.