Yes, the first thing that I did was to try tightening it... That wasn't the problem though. There has been no recent (at least 1.5 years) work on anything near the brake line or fittings, either. I removed the brake line and drove to NAPA (using emergency brake to stop), bought a replacement (fittings preinstalled, 3/16" x 30"; $7.15), installed it, and bled the brake system. It's fixed now, but I'd like to know why it failed. Inspection of the part didn't really shed any light on the situation. There were a lot of fitting options at NAPA. I think that the right one was labeled 3/16x 30" x p30.
O'Reillys lends out the brake line flaring tool, if you want to try that. I also tried to cut just the offending end off to reflare and use the existing fittings. Unfortunately their tool was out of square and wouldn't put a good flare on the end of the stock brake line.