This sounds like a carrier issue. Before doing anything to the phone I would call them and explain the issue. Sending email or receiving email from the phone should be the same.
If you send an email to another account is the email sender the expected name and system
If you were not able to send at any time even after configuring the account I would suspect the BB but because it works for 4 hours it seems to point to the email service or carrier.
You might configuring a new email account on yahoo or another free service and see if that works or does the same thing. IF it does I would call the carrier and make sure your account is set up correct.