My 3G connection suddenly died. Rebooting the phone did not fix it. So I said to myself, “uh oh, what now”?
This MacRumors post fixed my problem.
In summary, BossPrefs, which I had installed with Cydia just to toggle SSH, has some issues. Since I don’t want to use Edge, I had turned off the Edge display setting in BossPrefs. Turning it back on also re-activated 3G connections, fortunately.