If the lens coating is torn or worn of by extended use, is it possible to reapply it? I don't mean a do it yourself repair, but rather a repair performed by the manufacturer. It also may very well not be cheap, I realise that. Are there possibly some optical properties of the lens that are so delicate that they render a repair like this impossible?
Most likely not. The lens coating would have to be removed before it could be reapplied in most, if not all cases and that would likely end up deforming the lens itself. You could always completely replace the element if it is sufficiently damaged to be a problem, but it is unlikely that minor issues with the coating are going to cause significant issues.
I've had scratched anti-reflective coatings on eyeglass lenses removed in the past. Since the coating had been on the lenses for a few months it did not all come off but left a slight tint over the entire lenses. I chose not to have them re-coated because I figured I would also scratch the new coatings.
It would probably be more economical to replace the front element of the lens than to have the original coating removed and then reapplied. And since the manufacturer would likely not even consider doing such a repair, you would probably have to find a third party lab to do the work.
Whether that would be more economical that just replacing the entire lens would depend to a great extent on the value of the lens in question. It would probably cost more to have a sub $500 lens repaired with a new front element than it would cost to find another used copy for purchase. On the other hand, with a $1,000+ lens it would likely be cheaper to replace the front element.
There was a time when this service was offered -- even to the point of coating lenses that were originally made without coatings (this was a moderately common service for higher end lenses between about 1948 and 1955 -- the same time frame in which factories were refitting shutters with flash sync contacts).
The cleaning process required before coating (at that time) involved very careful repolishing, which would remove any existing coating, and from what I've read, both Schneider and Carl Zeiss Jena optical factories continued to offer recoating service for their own lenses (at least models still in production) as late as the 1970s, perhaps longer. This was only possible because they still possessed the figuring laps that had put the original curvatures on the lens surfaces, and the equipment to accurately (to a fraction of a wavelength) measure the final surface before applying the coating.
I've heard of this service being available recently, on a more generic basis, but I'm not certain I'd trust a shop other than the one that made the lens to ensure all the surfaces are correctly figured. In general, if the lens is expensive enough to be worth this treatment, it's too expensive to trust to an unproven process that still costs nearly as much as finding a good replacement.
It is, however, worth being aware that some pretty bad surface damage (especially on the front element) can have nearly no effect on the images produced. I've seen examples of lenses with significant chunks broken out of the front element, and the divot coated with black paint (to avoid stray refraction), being perfectly usable with a small exposure compensation for the lost area.
The effectiveness of lens coatings comes from their exact thickness, and the shared surfaces they have with both the glass (with known optical properties) and the air (with known optical properties), or in case of a multilayer coating, also coating to coating surfaces.
Wavelength/Half wavelength/Quarter wavelength based physickness and mathemagick are at play here. And you are measuring in nanometers.
Imagine the layers being tuned to a certain wavelength by their thickness - simply applying more won't make it more effective, but throw it out of tune. Adding an extra layer on top of an unknown material (if you tried to paint or spray a new coating over a damaged one) would give you unknown results. In the case of a scratched through coating layer, a layer added on top would both have interfaces with the underlaying glass or layer, depending on the exact spot - this would not improve anything. Also, you would end up with an even more uneven coating-to-air surface which would be optically very disadvantageous.