I have a Nexus S running 4.1.2. My phone is setup with my gmail account and two exchange accounts. One of these exchange accounts points to my zimbra+zpush mail server, the other points to my day-job exchange account.
A few weeks ago, my day-job exchange account stopped updating the email received in real-time. I however was able to send out no problem. I then proceeded to re-add the account in many different ways, including restarting the exchange server. I seem to be the only one affected. Whenever I have re-added my account it does still retrieve old email messages, but the "newest" email it retrieves is about 6 days old. It eventually gets newer messages, but seems to keep that 6 day gap. Calendars however seem to properly be updated for this account.
However, my zimbra+zpush mail is working properly. I receive email on my phone right away.
I'm not certain exactly what caused this, as nothing changed for my phone or the exchange server at the time the issue came up. The best explanation I can come up with is a DST skew, but I'm not sure how to correct this and why it hasn't been previously corrected.