As with most maintenance issues, the answer is always "it depends."
In my experience, you can probably cut the base of the mounds and part way up the slope at fairway height, as long as the slope is under 20%, maybe 16-17%, depending on grass type, with bent probably the most sensitive to cuts on slopes.
Also to factor in is areas where mowers turn, as a combo of stress factors seems to take turf out quickly. A combo of steep slope where the mower makes a tight turn would probably suffer. Of course, you need more irrigation, so sprinklers need to be nearby, and I have seen cases where fairways (or greens) facing into prevailing winds work less well on slopes than ones facing away.
Equipment might make a difference. I would guess if you did a clean up pass with a lighter mower on those slopes, it would be slightly better, depending on what you use in the fw. On the other hand, turf dying is sort of like being partly pregnant. It seems like once the stress factors add up, it is hard for it to survive in a weak condition for too long.
Others experience might vary, depending on location. It will be interesting to hear from the supers.