I've noticed something similar
I don't think I've had that problem with my safari not working, but email definitely stalls out sometimes. What I've always done to fix the problem is to kill all the running apps. For whatever reason I think that some of the other apps that use data, somehow interfere with the mail app being able to keep a constant connection with exchange. So the second all the apps that are running in the background, including the mail app, are killed I'll get a flood of emails come through all at once that got stuck on the server. If I kill all the apps and that still doesn't do it, then i'll do a hard reset on the phone and that will always fix it.