I re-read over all of your posts to make sure I had your issue fresh in my head (versus the comments of other users).
Just to recap you notice that after a few hours the email starts to arrive intermittently, and eventually the ActiveSync connection would stop working altogether.
You dropped the activities ActiveSync was doing down to just email and calendar, and things seem to stabilize for you.
The reason I asked what version of Exchange you were running is because the Notes synchronization wasn't introduced until Exchange 2010 (ActiveSync 14) and I wanted to make sure your device wasn't trying to use it and getting confused.
You asked at one point how could the issue be something server side if it worked fine on an Android device and not the BlackBerry Z10. There very well could be a difference in how the devices are reacting to the server's ActiveSync policy since they are from different product lines and support different features:
Comparison of Exchange ActiveSync clients - Wikipedia, the free encyclopedia
That being said I tend to think the issue is most likely with your device or the connection to the server since I have my Z10 hooked up to my Exchange 2010 SP2 (ActiveSync 14.2) server in my lab with 0 issues (and it is running in a resource limited VM).
If it is connection related, it could be something like a firewall in between your device and the server is timing out the connection before the BB thinks it should be, and the BB gets confused whereas the Android implementation on your other phone could potentially handle a situation like that better. This is pure conjecture, I have no idea if you are having a connection issue, if BB doesn't handle those well, if Android handles them better, just throwing out how this could be a "server" issue in the form of a connection to the server and how the devices might react differently.
That being said, my suggestion to you to troubleshoot the issue further is to turn on diagnostic logging on your ActiveSync connection when you see issues, and then try to get the device to update. The best instructions I have found for this so far are:
HOWTO: Visual guide to turn on Exchange ActiveSync mailbox logging through OWA - mstehle: The CDOs and CDONTS of Messaging Development - Site Home - MSDN Blogs
Hopefully that will show you if the requests are even making it to the server. If they are and your BB isn't handling them, then you should definitely open a ticket with BlackBerry as they will want to know and help troubleshoot the issue. If you device's refresh requests (and I would even go so far as to reboot it) aren't making it to the server, then I would look to see what might be in the path between your device and the Exchange server that could be impeding connection attempts after a period of time.
Sorry there is no magic bullet here.