UPDATE: I was having a somewhat different -- but related --issue. I was trying to sych with TWO different hotmail accounts using the HTC-supplied Android mail app.
One of them was synching fine. The other stopped downloading e-mail into the inbox and kept reloading an old, expired message from when it worked initially. I was still able to compose and send mail from that second hotmail account, but the inbox would simply not download any new mail from hotmail.
I deleted and added the account several times. It appeared to be an issue with the mail cache on the phone...that account keeps loading only an old e-mail it downloaded when it first worked last week.
I then tried both linking and unlinking the two hotmail accounts in hotmail itself to see if that made any difference...it didn't.
I was FINALLY able to fix the issue by turning ON the mail app's option to delete e-mails from the hotmail IMAP server and then turn it back OFF. I have no idea why that reset the synch, but now it works fine.
Weird.