The issue is now resolved and my connection with the AXBB-E is stable. Here is what I did to resolve the issue:

1. I was sharing the 5V DC Power Supply with several devices. I installed a dedicated power supply that feeds just the AXBB-E board. I believe the AXBB-E is sensitive to any fluctuation in voltage.

2. I updated the configuration as follows (please note that on my system I have the AXXBB-E board connected via a cross-over cable directly to my notebook's ethernet card): My ethernet port IP address was changed from a dynamically set IP to a static IP. This is exactly as per the manual. The static IP is 10.10.10.10 with a mask of 255.255.255.0. What I was confused about is that this is the IP address of the Ethernet Card (and not the AXBB-E Card). I then used the UCXX utility that comes with UCCNC to set the AXBB-E card IP to 10.10.10.11 with the same submask 255.255.255.0. This essentially establishes a local subnet consisting of the ethernet card and the AXXB-E card. After this revised configuration the "test connection" button on the UCXX utility is successful and CMD pings to both 10.10.10.10 and 10.10.10.11 are successful.

Hope this helps other users. It consumed many hours of head scratching to resolve.