Jasperpants is happy, now that his Scheduler is sweeping floors again, but, Why is it that no one is asking about the transistors that I early on claimed appeared to be weak? Did they 'heal' themselves?
No, they didn't need to be healed, or replaced, they weren't broken; answers the latter question. And, the answer to the first question could very well be: Not enough electronikers are critiquing these threads. Maybe none at all! I could very well have been just talking to jasperpants, and myself, throughout this thread!
Roomba-5XX owners (or their out-of-warranty repair person) should probably pay attention to the culminating technical information in this thread, because there is no reason for iRobot to not have copied 4XXX cliffs, wall, & caster-stasis circuits onto the 5XX's main_PWB asm! Only the names of the 'players' will have changed.
I'm just going to continue talking to myself, now that I have recognized why those Q4 and Q44 transistors were made to look bad; and perhaps, some future traveler, wending through the RR-archives, will come upon this post and won't fall into the 'hasty conclusion' trap!
Repeating the 'question', what caused those transistors to appear degraded? The short answer is: Transistor Q44 looked to be in trouble because Q4's output-load (the LED-string) was not connected! That missing load creating an impedance mis-match which then over-loaded Q44. Under that duress, measurement of Q4's signals became meaningless. (more on this, shortly)
If any 4XXX, with swivel-caster, owner runs into the symptoms of dark left-cliffs' LEDs, and dark swivel-caster (statis sensing) LED, the prudent testing is to first power-test that string of LEDs. Once that collector-load is known good, then worry about the behavior of its driver xstrs.
Advice is identical for Q37's two-LED string for Roombas right-side (outer) cliff & wall LEDs; as well as for left-side cliff-LEDs on non-swivel caster 4XXXs; however, the latter two zones do not employ the extra LED and its assembly design (i.e., PCB-mounted LED), which apparently weakened the swivel-caster's LED connection, hence, such open-circuit failures in non-swivel caster Roombas may be much less likely.
Further elaboration about this impedance mismatch, can now be discussed.
Some graphic aids have been assembled to support this discussion. One is a schematic diagram showing just the cliffs', wall-sensor's, and swivel-caster's LEDs' driver circuit. I call this diagram a "partial" Schematic_12 {Schematic12,Schematic#12}, because it does not incorporate the
detector portions of each of those sensors. The partial schematic is shown next in the required small image size, but a more readable size has also been attached:

This version also lacks connectivity information that can aid trouble-shooting, and that is unfortunate here because this sensor-group wiring is the most complex set within the 4XXX Roomba. Jacks J2, J8, J24, and the Bumper-jack J1 handle portions of off-board interconnections to corresponding remote sensor-heads. i believe no other Roomba sub-system requires that many connection interfaces!
A full Schematic_12 version will span an estimated four pages, to not only show associated photo-transistors, (PT), (the detectors which all seven LEDs illuminate), but will, in part, be a 'wiring-diagram' that shows wiring from plugs to remote sensor-modules.
The above schematic was drawn using a CAD, electronic-simulation program. Simulated circuit behavior will be shown at the end of this post, but, before viewing output data, it is important to have some notion about "input" data, to wit:
Other things about the schematic:
a) All part-labels and resistor values are those seen on the 2004-vintage main PCB / PWB-asm. The off-board LED device numbers are unknown, therefore visual-red LEDs, instead of 940 nm IR-LEDs, had to be put in the schematic to support signals' simulations. Simulations are then less-exact, but still show the devastating impact on circuit-function when one string of LEDs goes open-circuit.
b) A test-switch is shown in series with Q4's LED-string, but, that switch is not a real component. The normally-CLOSED switch will be set OPEN to simulate a disconnected LED-string.
c) Values of capacitance are unknown, however, the values shown were obtained by adjusting their simulated values until the circuit 'worked'.
d) Diode D28's P/N is unknown, and that is considered nonessential to the simulation; its just a voltage-clamp. SMD xstrs Q24, and Q44 are shown correctly. TO-92 cased xstrs Q4 and Q37, which are SS8050 types, are not in the simulator's database, so have been emulated by using the model of a nearly identical transistor -- the ZTX450.
e) A 50% duty-cycle, 1kHz, zero to plus five-volt stimulus signal is provided to the driver-circuit via the MCU, (micro controller unit) pin 54 of U8. Schematically, this signal source is simply shown as a simulated signal generator.
f) Q24 and Q44 are powered by Roombas +5VREG buss, while the output drivers Q4 and Q37 pull raw battery power through all the LEDs. V_batt was fixed at +15Vdc, for these simulations.
g) Note that Q44's output is dc-coupled to both output drivers, hence, if one output-driver is placed in a stressful mode, that stress will be reflected to the other driver, and also to Q44.
Under the above conditions, and with the indicated substitutions, two simulations were performed, one in which all LEDs were normally driven -- thus simulating normal operation, and the second was done with no collector load for xstr Q4 -- thus, emulating the fault in jasperpants' Scheduler.
The format of a simulator's output can look like that from a multichannel oscilloscope. See such multi-signals in this next image...

(which is also repeated in a larger image as the middle attachment, below)
...sample wave-forms from signal-points labeled on the schematic. All signals, except for the base-drive (V_Q44b) into Q44, are nominally 5VPP, in magnitude, and with flat top and bottom peaks. Only the signal "V_Q44b" requires a smaller total scale-range (of three volts). The test-switch is closed, so these data represent a normally operating cliffs', wall's, and (if present) swivel-caster stasis' LEDs' driver circuit.
A click of the test-switch sets it OPEN, thus making Q4's load infinite resistance, after which a second group of wave-form plots were captured. They are shown in this final image...

Now, the first feature change that might be noticed is the slight sloping of signals Q37e's, Q44c's, and Q4e's high-peaks, however, more importantly, the signals' peak-to-peak magnitudes of each of those three are drastically reduced! V_Q4e is down around half a volt, V_Q44c is not much more than one volt, and V_Q37e is similar.
I now recognize these effects to be due to the missing "transistor-action" of Q4! Q4, without any collector-load, behaves like a diode (the base-emitter diode) whose current is limited by the sum of its base input resistor plus its emitter resistor. Base current is then higher than when the dc-gain of the transistor allows base-current to remain very low while the higher, controlled, current(s) pass through the collector-emitter junction. Q4's action looked faulty simply because it had no collector-load! Then, it was the oversize Q4-base-current that overloaded Q44's output to then make it, and Q37 appear to be degraded.
============ Q.E.D. ==============