The satellite constellation is fixed, while the Earth rotates inside it. Thus the number of satellites you can see, and the declination and azimuth of those satellites, will change during the day (and with your location). Some locations and times are better than others - especially if there is a satellite outage in your area.
To expand on Capt Bloggs useful remark...
Global Positioning System - Wikipedia, the free encyclopedia
The satellite constellation can be varied, and the satellites do rotate around a rotating earth if you believe Wikipedia (at twice the earth's speed). The satellites are not fixed in space relative to the earth, if that's what you mean. Their altitudes are about 3 times the diameter of the earth, so this helps coverage greatly. The official websites do say that 6 should be available
almost anywhere on earth, but if you read some websites, it says that these satellites should be "above the horizon". If you're in a deep valley or flying below the top of a mountain range, your horizon may well be limited. With a satellite out, perhaps GPS coverage could get pretty sparse. However, depending on your navigation system, your map position shouldn't suddenly start moving sideways to the pure IRS position when you lose your GPS. The nav system should maintain a constant bias towards the previous radio-based position until you reacquire a new radio position or the system is reset. The difference is not (normally) suddenly washed out.