I'm not sure but I think you need to add in avast4.ini ports 1401 and 1402.
Also I don't think that avast! is the reason of this problem. Do you have a firewall?
This ports aren't constant values, see more big stunnel log
2007.01.14 02:36:25 LOG5[3536:1840]: gmail-pop3s accepted connection from 127.0.0.1:1351
2007.01.14 02:36:25 LOG5[3536:1840]: gmail-pop3s connected remote server from 10.126.1.2:1352
2007.01.14 02:36:31 LOG5[3536:1840]: Connection closed: 72 bytes sent to SSL, 252 bytes sent to socket
2007.01.14 02:41:26 LOG5[3536:2276]: gmail-pop3s accepted connection from 127.0.0.1:1360
2007.01.14 02:41:26 LOG5[3536:2276]: gmail-pop3s connected remote server from 10.126.1.2:1361
2007.01.14 02:41:27 LOG5[3536:2276]: Connection closed: 66 bytes sent to SSL, 217 bytes sent to socket
2007.01.14 02:46:26 LOG5[3536:2384]: gmail-pop3s accepted connection from 127.0.0.1:1370
2007.01.14 02:46:26 LOG5[3536:2384]: gmail-pop3s connected remote server from 10.126.1.2:1371
2007.01.14 02:46:27 LOG5[3536:2384]: Connection closed: 66 bytes sent to SSL, 216 bytes sent to socket
2007.01.14 02:51:26 LOG5[3536:2544]: gmail-pop3s accepted connection from 127.0.0.1:1392
2007.01.14 02:51:26 LOG5[3536:2544]: gmail-pop3s connected remote server from 10.126.1.2:1393
2007.01.14 02:51:27 LOG5[3536:2544]: Connection closed: 66 bytes sent to SSL, 217 bytes sent to socket
2007.01.14 02:56:26 LOG5[3536:304]: gmail-pop3s accepted connection from 127.0.0.1:1394
2007.01.14 02:56:26 LOG5[3536:304]: gmail-pop3s connected remote server from 10.126.1.2:1395
2007.01.14 02:56:27 LOG5[3536:304]: Connection closed: 66 bytes sent to SSL, 217 bytes sent to socket
2007.01.14 03:01:26 LOG5[3536:3008]: gmail-pop3s accepted connection from 127.0.0.1:1399
2007.01.14 03:01:26 LOG5[3536:3008]: gmail-pop3s connected remote server from 10.126.1.2:1400
2007.01.14 03:01:27 LOG5[3536:3008]: Connection closed: 66 bytes sent to SSL, 217 bytes sent to socket
2007.01.14 03:04:06 LOG5[3536:2344]: gmail-pop3s accepted connection from 127.0.0.1:1401
2007.01.14 03:04:06 LOG5[3536:2344]: gmail-pop3s connected remote server from 10.126.1.2:1402
2007.01.14 03:04:07 LOG5[3536:2344]: Connection closed: 66 bytes sent to SSL, 216 bytes sent to socket