Try using Wireshark to capture traffic between the devices. You can use the tshark command line utility that is included if you wish to capture round-robin type files and then copy off the captures when the event happens. There might be some content in those captures that can tell you what is happening. Another thing to watch is some of the perfmon counters on the web server. Specific perfmon counters could include user connections, w3wp process utilization. You might also look to see if additional website logging can be enabled. Do a search on Microsoft KB articles about debugging IIS issues.
Ping results only say if the NIC is online with an IP address and is listening to ICMP. There is something happening with the web server as you already know. Try also using the hping tool to “ping” port 80 and 81. This will also help track down when the service is not available.