Throughout the world of work, falling asleep at your post is a grave offense. With one exception. I had a friend in my freshman year who worked the night shift at a hotel. Few people showed up at night, so he could sleep most of the time, but he had to wake up in a hurry if someone did show up wanting a room. He was quite alert, even in his sleep. He would fall asleep in class, and when the professors angrily woke him up, they were surprised when he could recite the lecture, verbatim.
However, other studies have shown that sleeping while under the stress of a problem actually helps solve it. When Russian astronauts have an insurmountable problem, they take a 15 minute nap. The solution usually occurs to them by the time they wake. Businesses should definitely harness this phenomenon
In Japan, a cheap form of hotel is available that they call a "capsule hotel." A room at this hotel is actually just a bedded tube. For a comparatively cheap deposit, one may sleep in the tube. Such a hotel uses very little space, which is at a premium in Japan. People appreciate it when they're stranded, because it may not be luxurious, but it does give you a good night's sleep for a low low price.
I think businesses should have a small capsule hotel built into them, and send people there for a 15 minute nap anytime an insurmountable problem arises. Workers will awake partially refreshed, and possibly with a solution at hand. If they don't have a solution, they will at least be in better shape for finding one.