Just wanted to let you know that, while the suggestions did not solve my problem, they did provide enough information for me to constantly monitor the issue. I conclude that I have 1 port on the switch that was creating all my havoc (port 7). By using the web interface:

I was able to monitor and I saw that if I attempted to use port 7, all my devices would suffer drops. Is there anything further that I can do to look at that port in particular?