If you still have one of the older versions (paid versions) try that. Version 5.1 never really worked properly for me but 4.5f is still going strong, week after week, now on 4.2.0 PL2.
Otherwise, please give me details about your settings and I'll try to figure it out.
One recommendation to try is this:
AdminCP >> Settings >> Email Options
Use Mailqueue System = No
Use Cron Based Sending = No
Number of Emails to Send Per Batch = 1000 (tweak this if it creates problems on your server)
E-Mail Send Delay = None (tweak this if it creates problems on your server)
Encode as UTF-8 = No
SMTP Email = No