We've done some further investigation and confirmed this is an AVG issue.
The AVG client (Business Edition 9) includes an "Online Shield" service, which innocuously claims to protect Web and Instant Messaging traffic. Last month the client had upgraded from 8.5 to 9.0 and restarted the server (no problems yet). After the 2nd restart last week, the problem arose.
While we had an Outlook session open to the server over SSL, we turned this service off in AVG and every Outlook connection issue resolved within a couple seconds.
I'd recommend disabling this service (and other "client PC" intended modules like LinkScanner) in AVG 9.
Note: this module is available in every version of AVG 9 (Business edition, Internet Security, etc.) with the possible exception of "Free".