Any resolution to this issue? I'm having exactly the same problem with 3.1-RC1. If I revert to 3.03 the issue disappears and my static homepage works as expected.
I've been doing some experimenting with my permalink structure and this is the behaviour I've noticed so far:
If I use the default permalink structure (or any of the preset options), the problem disappears.
If I set a custom permalink structure with the format /%postname/ or /%category%/%postname/ the problem reappears.
If I set a custom permalink structure with the format /articles/%postname/ the problem disappears.
Curiously, it seems that including a static element in the custom permalink solves the problem, whatever it is.
I first noticed the problem in a theme I'm developing myself at the moment but I've checked with TwentyTen and the behaviour seems identical.