We have a Cisco ASA 5510 (47-7523-01 Rev A0) that we are using so that users can connect to the VPN from home.
I use this connection myself to do late night backups on our old database systems that don't quiesce.
It worked fine until this week, but now it seems everyone is getting kicked off at once, probably about 12 people on at the same time.
I'm told by my fellow IT guy who's been here six months longer than me that the VPN connection is 10MB down and 10MB up.
I also recorded some logs when I was having trouble staying connected myself, and I took notes that corresponded to the log number and what was happening. I don't know enough about VPNs to see if they are safe to post or not.
That said I have found a couple of articles on your site about how to configure and setup a VPN with an ASA, and I'm going to take a look at them.
I read somewhere else that the connection speed might be the problem, but I don't know it for a fact...