I opened a support call and spoke with an Apple Technician. He had never heard of this and could find nothing online about it. My goal with this post is to document the problem, and show that the Logitech Keyboard was related to the problem. The solution, unfortunately, was iPad replacement outside of warranty for $299 plus tax. The repacement went smoothly, once at the local Apple Store. I made an appointment and showed up on time. I backed up the iPad with iTunes. The Apple Store technician had never seen the problem before and said it was hardware failure - could not be repaired at the store. Replacement required. Problem was 100% reproducible in front of technician.
One extra issue I had was the iPad was from my company, and there was security software installed with an Admin account and password. I had to call our data center on a Sunday afternoon and get the password so the iPad could be wiped clean before turning it in.
Restored from iTunes, and had to redownload a few apps for accessing the corporate network, and the iPad had cellular, so the SIM card had to be switched, and AT&T had to reassociate the IMEI number with our coporate account.
All is well now - new iPad, cellular working, apps reinstalled...I'm productive again. I hope this post helps others.