(This is an edited version of the message sent to support, along with an screenshot that has all location specific information removed. All location specific information has been replaced by (source) and (destination). For those interested, note that the two locations in question are both on the east coast of the US, so physical distance is not a contributor to this problem).
Pete:
I posted the question about pinging the router gateway. The (destination) office has Comcast. They have a Linksys BEFSR41 router connected to a brand new RCA modem connected to Comcast. For the last two weeks, they have constant lost their VPN connection to the server in (source). The IP address for (destination) is (destination). The IP address for the (source) office (with a Cisco router) is (source). After much testing, I do NOT believe that the problem is in (source). Other offices are able to connect without a problem.
At Comcast's insistence, we replaced a Watchguard SOHO with the Linksys. No improvement. I've pinged the Linksys as a separate process as you suggested and got a 0ms reply (is that no reply?) Since I cannot interpret these results adequately, I have no idea where the problem is.
I've purchased multiple copies of PingPlotter for myself and others as I am quite impressed with it.