Yes, i am having this problem too.
I have the Verizon HTC thunderbolt and use the HTC mail app.
Description of problem: Settings are set so that during "peak" hours, the email should download every 10 minutes). However, the emails do not download every 10 minutes. When i notice that i haven't received any emails, even though i know i should have received some, i open the HTC mail app and that starts a sync with the server and it downloads all available emails. Double check settings, wait an hour and repeat; the same thing happens (won't download unless i open the htc mail app)
These symptoms first happened to me around the time i got the gingerbread update (late summer). I went in to the settings and changed the send receive time to something different (10 min to 15 min or something like that), then it worked as expected. Then in late December I got another OTA update (updated from 605.5 to 605.9 still gingerbread) and after the update, it happened again where it would not update at the specified interval during work hours. So i went in to the settings and changed the send receive time to something different again (like above) and it worked as expected again. So you'd think that would fix the problem right... ( FYI, up to this point i am running full stock experience direct from verizon/HTC)
Well, i rooted my thunderbolt a week ago (used revolutionary.io so i had to downgrade from 605.9 down to 605.5, then rooted. Still running the stock ROM, but rooted 605.5 - i'll get to baked custom roms later). Anyways, after i rooted, the problem happened again, so i did what worked twice before... BUT it only kinda works. I use HTC mail app to keep track of 2 email accounts: personal and work. The personal account (imap) is working as expected, but the work account (pop) is not. The work email (pop) only updates when the htc mail app is opened.
Bottom line, Yes i'm having the same problem, does any one have a REAL fix for this instead of me bumbling around the phone and accidentally finding something that kinda works?