derek collier- This is one of those questions that nobody can really answer, and no, that's not a blow-off
Generally speaking, machines like the UDM are pretty gentle, and most paints can easily withstand dozens of gentle polishings.
BUT...if you're effecting serious, complete correction, where you polish the clear down to where it's level with the bottom of deepish scratches, then you're taking off a lot of clear no matter what machine/technique you use.
If you remove more than 0.03-0.05 of a mil (that's 0.0003-5", which isn't much) then you'll probably precipitate clearcoat failure, and you can have other issues too, like fading of the colorcoat under the remaining clear.
So my advice is to polish it as little/gently as possible, as infrequently as possible, while still doing it aggressively/often enough that your vehicle looks OK to you. Which sorta boils down to not marring it in the first place, well.. as best you can in the real world.