Matt,
As Jim stated and you know, login information is stored on the site and in cookie files on your computer. If something happens to the cookie file (deleted or blocked), the system will have no idea who you are.
However, that being said, your loss of a "session" is more than likely related to possibly your IP address changing while you are connected to the site. Since you are accessing the site from work, you are most likely going through some company firewall/portal/vpn/etc. to access the "wild" internet. If your IP address changes while accessing the site, the forum will not recognize your connection and block the session cookie. Currently, the site validates IP addresses using the first two digits of your IP address.
For example,
IP address 192.168.1.1 would be checked for 192.168.x.x. Any change to the last two digits would be allowed, however if one or both of the first two changes, it's a different connection and a possible security risk and the session cookie would be invalid.
You can do some tests on Google by typing "whats my ip" in the search box. If you do that several times and it keeps changing, that is the likely cause of your drops.
Dennis