Hi Richard,
I'm starting to think it may point to the hand-off to the cell. carriers. I'm also on my second iPad, and the behavior is pretty much the same (although at times a little different).
I currently seem to mostly experience the following problem: when I change from a cell. tower to another, mostly when I go from one supporting 3G to one supporting LTE, I negotiate only with about 1 or 2 bars. Just turning the LTE off allows me to renogotiate to 5 bars on 3G. Re-enabling the LTE usually brings back 5 bars and 3G, but if it's LTE service I get, it very rarely goes beyond 2 bars, but connectivity is still good. Going from WiFi to 3G doesn't seem to be much of a problem though (although it did happen).
It's only been about two weeks, with two different iPads, but my problems seem a little different than most on this thread. I did get the 5 bars, 3G logo and no connectivity issue a lot last week, but this seems to have been resolved.
I'm reminded at how similar the iPhone 3G support was here in Canada, as they were just rolling out 3G. I'm starting to seriously think it's a carrier issue which should be resolved as time goes by.
I hope so for all our sake.
Regards.