Turtle,
Yes they should be able to determine what is coincidently wearing out vs outright abuse of things like hallway doors on the 7th floor or the cab doors getting beat up or buttons being broken. Construction elevators, which your is not, can suffer from doors being hit and knocked out of alignment which then result in doors that do not close fully or properly and possible entrapments may ocurr.
The guys are right in that a construction car will take or suffer a bit due to the types of materials being transported to the egress floor for removal. Not knowing the real condition of your equipment, roller guides do wear out. From improper loading? Maybe, maybe not.
Your service guy, if it has been the same person for a few years should be able to determine whether failures are normal wear and tear, or failed do to other factors. Other things may ocurr with improper loading, but I don't believe drive problems or rollers unless they were in a pre state of failure before your renovations commenced...three years ago.
One way your equipment will suffer is due to the excessive dust and construction materials being trucked across the landing sill, and this may be in part responsible for entrapments. But I'm only guessing. Failed Drive Cooling Fans will cause shut downs and entrapments.
The age of your buildings equipment, the degree of maintenance it has received in the past, and is receiving now and the responsibility of the GC on the renovation project all come into play.
All "Billable Due to Construction" tickets should be the responsibility of the GC if the trouble can be proven to be construction related, as he has taken your elevator to use for his project, subjecting it to what may be defined as extreme invironments which your equipment is not normally exposed to.
Dust (construction dirt) is temporary, but it is also accumlitive. Over time it will affect a number of operations mechanical and electrical, and typically, your maintenance agreement won't cover the extra time to vacuum or brush out excess dust, so it is what it is.
The issues you cited i.e drive fans, relays, rollers, May be normal wear issues. However, if your equipment has a penthouse on the roof, construction dirt and dust will be drawn up through the the openings in the floor leading to the machinery space, and ultimately the drive fans will suck it up, quite possibly leading to overheating of the drive unit itself. Could they have failed due to excessive use or dirt/dust? Does the equipment room look as though a dust storm has hit it week after week (slight exaggeration) for three years? Excess dirt/dust may be a cause. Visual inspection may reveal clues, and it may or may not be obvious to you. Again, the age and condition of the equipment before the job started plays a role here and the overall environment your equipment is and has been subject to for three years is important in determining the outcome.
Talk to your service provider and see what can be done to keep things rolling smooth for the duration.

Just my dollar and 22 cents worth.