I think I know what is happening, because I ran into the same problem around two hours ago. We have a timing problem in the app where Android will "toss" some things that we are still using. I am working on a fix for it.
The workaround I use is to enable calibre debug mode, connect, and then wait until calibre starts sending NOOPs to the app. The app will show a force close dialog in the middle of this, but don't hit OK until you see the NOOPs on calibre's debug log. From then on the app will then be stable until you send more books or until you change libraries to another that has the books in it. There is nothing more you can do until we get the update out, which will be sometime tomorrow (UK time).
My apologies. This bug is my fault. I added on Friday some internal caching of metadata to speed up the app (it got more than twice as fast), but I broke something fundamental.
Thank you for your patience.