I have spent the last two weeks in the Buellton, California Marriott hotel. I have had nothing but frustrating problems with my iPad Wi-Fi connection. The iPad portability allowed me to wonder down the hotel halls looking for a signal sweet spot which I would eventually find. I switched rooms trying to get closer to the router. This didn't seem to help much. I finally decided to do a side-by-side test and set up my work laptop (an HP) next to my iPad. The HP shows "Good" signal strength, and I had no problem getting on the internet and finding your site on iPad signal strength issues.
My experience also corroborates your theory that signal strength is compromised when the iPad is lying flat. I noticed when the iPad is flat on the desk, it will not make a connection. When I prop it up in the vertical position, I get better reception, but it is still intermittent with frequent dropouts.
This problem has been such a frustration and such a disappointment that I am seriously considering returning my iPad and getting my money back.