Your ISP I wouldn't think would be able to help.
The error message seems to be incomplete as it usually indicates what program/process is hogging the connections.
This can be down to another AV or remnants, news reader/aggregater, anti-spam, etc. do you have anything like that ?
Concurrent Connections Error: You could modify the avast4.ini file using notepad, "C:\Program Files\Alwil Software\Avast4\DATA\avast4.ini." Find the [MailScanner] section and insert a new line after the section heading, and enter this MaxConnections=50 (if that line exists you can change the value to 50). Save the changes, the avast self-defence will ask if it is OK answer yes.
[MailScanner]
MaxConnections=50
The default concurrent connection limit is 20 (for mail & news together). If the limit was exceeded, you would see the line Closing connection due to MaxConnections into aswMaiSv.log file. This limit exists not to save resources, but to prevent connection looping in strange configurations, so the user can increase it without worry to, for instance, 50. The value 0 disables the limit.
However, you should endeavour to find the real culprit rather than extend the limit as it is likely to gobble up the extra connections.