I was repairing a piece of old equipment, and needed a replacement RF
transistor. Checking at Digi-Key, I found very thin pickings, so i checked
a few other distributors, and found the same situation. They seemed to have
a modest choice of SMT transistors, but REALLY thin variety in T0-92 and
similar plastic packages. Not a good sign, as we have a lot of 30 - 40 year
old nuclear instrumentation here.

Yup. The last five years or so have been dire times for through-hole
semiconductors. A lot of the popular parts are now gone, past the
end of the "lifetime buy" cycle from their original manufacturers.

I've been trying to stock up my own (hobbyist-level) supplies of
useful TO-92 transistors - a mix of general-purpose jellybeans, RF
amps, JFETs, and low-noise audio parts - whenever I can. I figure
that a bag of 100 of any particular type constitutes a "lifetime buy"
for me.

For parts that have only recently gone obsolete, you might want to
check with Rochester Electronics. They seem to have a pretty good
stock of a lot of parts that Digi-Key and Mouser have dropped.
There's a $100 line-order minimum, but it might be worth selecting a
few useful parts and investing some $$ in a lifetime stock.

Another issue is the circuit is a differential NPN pair set up as a one-
shot. So, it was running about 23 mA through one transistor at idle, and
all of these on-at-idle transistors have failed. (The other transistors in
the pairs seem fine.) The part actually in the unit is an FMT1190, which
certainly seems like it should have been able to handle that current long-
term. After replacing it with the best thing I could find, the transistor
only has about 2V C-E, so the power dissipation is less than 50 mW,
shouldn't have burned them out. I'm wondering if somehow the startup
condition exceeded the base ratings.

Maybe a short inverse spike condition during powerup, which
reverse-biases the base and makes it avalanche?

Or, is there any chance that when the one-shot fires, the transitions
are slow enough that the transistor passes outside of its SOA while
turning on or off?