I am having the same issue with GMail. I stopped getting messages at about 4:00PM. I have tried a few work arounds. Here's one from BB's website
Gmail removes messages from the Post Office Protocol (POP3) server when accessed by a BlackBerry Internet Service for T-Mobile integration.
Set up mail forwarding to your BlackBerry Internet Service address.
Log in to the BlackBerry Internet Service for T-Mobile account, and delete the existing Gmail integration.
Create a BlackBerry Internet Service for T-Mobile hosted mailbox (firstname.lastname@example.org). For instructions see KB-04478.
Edit this account so that the email field contains
. Now, messages sent from your BlackBerry® wireless device will appear to have originated from your Gmail account.
Log in to Gmail. Go to Settings > Forwarding and POP.
Select the Forward a copy of incoming mail to... option and type
Select Keep Gmail’s copy in the inbox.
Not sure if this will help.
8100 (T-Mobile, Texas)