The question of how long a whale can survive out of water has a variable answer because it depends on a few things. Smaller whales (like pilot whales) can probably last longer than bigger whales just because they aren't as heavy.
The problem all whales have out of water is that their bones just aren't designed to support their weight on land - since in the water they don't have to give much support. Thus, cetacean bones are light and porous. So on a beach a stranded whale will literally crush itself under its own weight.
As for how long a whale can actually survive, it's a few hours for a large whale, in some cases longer; depends on air temperature and how sick the whale is to begin with. Single whales strand almost always because they're close to death anyway from some other cause.
Whales that are kept cool by people with cold water can survive longer. In the case of pilot whales, three animals that were released six months after a mass stranding on Cape Cod in 1986 had been on a beach for several hours. One of them was on the beach at least eight hours, but was tended for most of that time - people kept it cool, and maybe even rolled it around a bit from time to time so that its whole weight wasn’t bearing down on one spot.
Why can’t whales survive on land? Visit Whalefacts.org to find out.