The default concurrent connection limit is 20 (for mail & news together). If the limit was exceeded, you would see "Closing connection due to MaxConnections" in log file (Avast4\DATA\log\aswMaiSv.log). The limit exist not to save resources, but to prevent connection looping in strange configurations, so you can increase it without worry. Insert such a line to file avast4.ini under [MailScanner]:
MaxConnections=50
(the value of 0 disables the limit)