Mine on JB is acting normally. I played with it quite a bit yesterday and never noticed a drop out. I hate to say it, but Trophy's suggestion of a factory reset is probably the next thing to try. It's a fairly common thing to have to do after a major upgrade like this. It's a PITA because you then have to set up everything on your phone again.
In case you don't know, a factory reset in this instance won't actually make your phone look like it did from the factory. It will still be running JB after the reset. What it does is wipe all of your personal settings and apps from the phone.