When everything is aligned properly, I would take a reference alignment shot at your first external mirror, and at the cutting head. Then when you have cutting issues, check the alignment on that first mirror again and compare with original shot. If it moved, then beam coming out of resonator is moving. If it is still good, check alignment at the head; if that one moved, then external optics are the problem.
However, depending on the machine configuration you have, the distance between resonator output and first mirror may be very short; so even if the beam coming out of resonator did shift a bit, you may not be able to tell. That's were mode shots would be more interesting. If internal optics shifted, your mode would change, and you would see it on the mode shot.
If you're not sure how to take a mode shot, you can also check parameter 15204 (calibration coef). If you see a big jump in it's value after the alignment shifts, it could indicate something shifted internally. of course, you need to shut down, then restart the resonator in order for the system to go through its calibration and recalculate that parameter.
What are the Amada techs doing to get the machine back up and running? Are they adjusting the mode, or are they only aligning the external optics?
I have personally never experienced a beam shifting due to internal optics on Fanuc resonators. But in the case of short beam path, the Fanuc resonator can have 2 small mirrors inside the resonator (they reflect the beam to make the optical path longer), but they are not part of the internal optics (although they are inside the resonator). I have seen beam shifting due to those 2 little optics. If your machine has those 2 optics, you could try to cut the ties holding the water cooling lines attached to the frame (leave the cooling lines hanging free); sometimes, chiller start/stop and vibration from water circulation can make those mirror vibrate a bit and knock off alignment (I have seen this once). Make sure the spring loaded screws are completely screwed in (so spring is compressed to the max). Also make sure the 3 big bolts holding the plate where those 2 mirrors are mounted are tight. I've had them a bit loose once and beam would shift just enough to cause problems.
Also make sure your machine foundation is good. Do you have heavy punch presses close by the machine? If so, make sure you have cut an isolation around the machine foundation, and filled up with insulation material (rubber or Teflon).
Could there be a cooling issues which could overheat your optics and shift them? You could use an infrared temp probe and check your mirror blocks right after cutting at full power for a while. Temperature should be close to chiller temp setting.
Is the resonator properly attached to the machine frame or floor?
Are all the mirror blocks attached properly?
I agree with you, seems more likely that this is an external optics issue. I think the best is to take alignment reference shots are each mirror block. Then compare with same shots taken once the beam shifts.
If you still can't find out which mirror is the problem, you could try to push and shake each mirror block one at a time, trying to make them vibrate a bit; then take another shot at the head. It should not shift; if it does, the mirror you just pushed is the problem. Do the same for each mirror block.
The story about replacing the blower seems weird. If the blower was bad, it would project oil or debris internally, on all your optics. So if that was their explanation, I hope they also replaced all the internal optics. Taking a cold and hot mode would have also shown big signs of degradation if that was the case. Did they take a cold and hot mode?
Also, your calibration coef (param 15204) would have been going up; and you should have gotten power down alarms. Either they are not telling you everything, or the service engineer just did it so he did something...