In this case, when the pressure was at about 6 psi, I could feel and hear the air coming out. I bumped the pressure a little, and I guess the higher pressure sealed the diaphragm a little better, but when I sprayed the hole with StarSan it still blew bubbles, so there was still a leak.
If you're using flare fittings, make sure you're using flare washers anywhere there's metal on metal (everywhere but on the keg disconnects). For the various threaded connections, I used teflon tape and some pipe dope on everything. After that, StarSan solution or soapy water is my first test for leaks. Even slow ones should bubble, though they might be really tiny. Spray anywhere that has a connection and inspect thoroughly for even tiny bubbles.
Here's my general technique:
First, start with the CO2-in turned on, but the CO2-out off, so that only the regulators are pressurized. Turn off the CO2-in and let the regulator hold pressure, overnight if need be. If the pressure drops, obviously there's a leak. Re-pressurize, leaving the CO2 on this time, and spray all connections - between fittings, between the dial, the ball valve, and the various relief valves on the front and back. It may even help to try both higher and lower pressure, say 4 and 20 psi. Probably best not to leave the CO2 on overnight this time.
If the regulators are leaking from a connection, reapply teflon tape/pipe dope, and try again. If the leak is coming from the regulator body itself, apparently you need to rebuild it.
If the regulators hold pressure, then the leak is further down the line. Again, assuming a multi-body secondary (and assuming you have on/off valves on each regulator), pressurize one line at a time while disconnected from the keg, with the disconnect connected to the line, NOT the keg. Spray each connection with StarSan solution. Inspect.
If all your lines hold pressure, then you have a leaky keg. Pressurize, spray all connections with StarSan, and inspect.
It's a tedious process, but my 5lb CO2 tank lasted a good long time until this leak occurred. But now all seems well again.