In TOS, warp eight was indeed supposed to be a major problem if sustained for hours at an end, from "Arena" onwards at least. And Scotty said that even "sustained warp seven" would be "dangerous". But he was probably being a bit conservative there, as warp nine could be sustained for two-three hours in "Paradise Syndrome" and still the ship had enough power to tractor an asteroid or fire phasers before everything fell apart.
(Incidentally, judging by that latter example, it's the powerplant that fails first, and the dilithium might be the thing that fails first within the powerplant. The actual drive system, the warp coils and whatnot, can apparently take a lot more.)
The supposedly important intercept mission in ST:TMP was also run at warp 7, suggesting things hadn't improved all that much between the TV show and the movies.
As for exact numbers, it's almost impossible to tell. In "Arena", warp seven is apparently only sustained for some minutes, during which Kirk delivers a monologue; it's unlikely there would be major cuts there. Warp eight is actually sustained slightly longer, in a hot pursuit sequence where there definitely shouldn't be major cuts. But against the ability to sustain warp nine for "hours", or warp ten for something like five minutes in "Let That Be Your Last Battlefield", this evidence proves next to nothing. We never actually see the ship's engines burn out from warp travel.
Timo Saloniemi