After a few minutes, the 50V supply crashed.. and
guess what? The HOT base
 signal actually increased a bit, to around 250mV P-P while the collector
 fell by at least an order of magnitude.
 So please correct me if my conclusions are unwarranted, but I believe the
 situation is quite clear, now. The  HOT has a thermal intermittent in the
 E-C circuit - I just can't see any other explanation for this behavior. The
 base signal didn't flicker, it actually +rose+ as the collector signal went
 away. It's as if the E-C circuit is going high-impedance while the B-C
 circuit remains intact. 
That base amplitude sounds a bit low to me, I would have expected about 0.6V. But without
seeing the waveform it's hard to be sure..
BUT...
Remember that the forward voltage drop of a semiconductor junction -- like the B-E
junction of
the HOT -- depends on temperature. Diodes have actually been used as temperature
sensors due to this effect. So if the HOT is overheating for any reason the base drive
may appear to increase.
Yes, it's worth replacing the HOT. But don't be too surprised if it doesn't
cure it.
-tony