Telnet through VPN connection keeps dropping

We use a program called Tiny Term from Century Software, which uses Telnet through a VPN connection to connect to corporate servers in another state.  After users login using their account information, the connection is dropped after 2-5 minutes.  The time varies, and when it happens, ALL connections for this program stop.  By that, I mean each workstation running this program stops responding on every machine.

But not the Internet.  If I run a continuous ping from one station, login to Tiny Term, and monitor the progress of the ping, it never drops while the Telnet connection does.  This is a small store, and it is setup with the following:

DSL provided modem/router>Cisco Secure Pix 506>SMC Switch>Workstations (all running XP Pro)

This all started last week, and I have done the following:  Confirmed that network connectivity during this to the Internet does NOT go down.  Ran spyware scans and anti-virus scans.  Called corporate to check the firewall out, and was told traffic looked good.  Called the ISP to check their side out, and was told their side good.  Removed the SMC switch and replaced with another, left all workstations unplugged from new switch, and plugged in a newly setup workstation, never before on this network, with a fresh install of Tiny Term.

And still, it did the same thing.  Removing the switch and workstations would seem to me, to remove our internal network from the equation.  To me, it would seem to be some sort of setting within either the firewall or modem/router.  But what?

How would I monitor this type of program and the traffic that it generates, bearing in mind I do not have access to the firewall?  How would I monitor the connection when it drops?  What would I look for?  Any help would be greatly appreciated, as users are tired of constantly signing back in.

Thanks