I have experience only with Cameca WDS and its FPC. While I have no idea how old FEI WDS are made, maybe some of failure modes known to my experience could hint something.
I guess it is 1 atm FPC? Those then use thin grid supported film for isolation of P10 gas from escaping into the vacuum.
Is there a bubbler at the end of P10 gas exhaust from the spectrometer? In our WDS case we close the gas inlet, wait for pressure in inlet to drop and if we see then backward bubbles being sucked into the spectrometer - it is clear then - the window has a hole (or critical number of holes). Also wrong gas, back flow of atmospheric gas into spectrometer (i.e. gas closed for long term) can lead to suppression of townsend avalanche (ions recombine with electrons after ionisation instantly suppressing the avalanche) or grow into continuous glow discharge.
The next thing which could fail is HV generator and powering and voltage buffer line of the anode wire. One of failure modes of capacitors is "shorted" (normally capacitor is "open circuit" for DC) and thus would short high voltage with ground. The resistors sometimes can fail to making it "open". As wire in FPC then in both cases would never get high enough voltage - no Townsend avalanches would be produced -> no counts.
Finally, preamplifier is just 1st step. The shapping amplifier follows it. If there would be a way to see if shapping amplifier or preamplifier generates pulses (or cascades in case of pre-amplifier) it would be then clear that counting electronics malfunction. Signal from shapping amplifier is easy to get, with not much influencing the signal. probing preamplifier directly with oscilloscope howere is much harder thing.
When troubleshooting FPC there are two things to be aware: deadly high voltage!, and very sensitive signal path in preamplifier. For the first then rather resistance is checked of components after completely physically powering down and disconnecting supply to the HV generator and taking all precaucious that the capacitors are discharged. Albeit, measuring resistance of capacitor at low voltage with multimeter could miss the shorting seen at the high voltage. For the second point - connecting probe wires to preamplifier can mess with preamplifier circuit as it is very much succeptible to the capacitance added by probe wires.
Finally FPC can age (I am not sure how much that is possible on the SEM) especially when running at very high count rate continuously. It is well known process from CERN and seems P10 gas byproducts from ionisation can get deposited on anode wire and the cathode walls, and in both cases it makes the operation of GFPC worse and worse (It affects PHA mostly and is recognizable by growth of broad distribution at higher energy in PHA). However despite contamination the FPC should still function - it is long term deterioration of counter rather than instantaneous failure.