Remains Are Exposed
If the animal isn't covered with sediment right away and instead stays on the surface, the remains can suffer predation from scavengers that carry some of the bones away. A complete skeleton will not be preserved. An animal that dies, is washed down into a river bottom during a flood and is quickly covered with silt has a much better chance of becoming a fossil than one whose bones stay on the surface exposed to weather and temperature changes.
High-Energy Water Environment
Quiet bodies of water such as a bog, swamp or deep sea floor are preferable for fossil formation compared to high-energy bodies such as rushing rivers where the remains can be tumbled and broken apart. Oxygen in the water hastens bacterial decomposition of organic material. Fast-moving waters have plentiful oxygen. A cool, sluggish body of water is deprived of oxygen, causing the decomposition rate to slow significantly.
Coarse-Grained Sediments
The potential for damage to the animal's remains from being tumbled in moving water is magnified if the sediments have coarse, sharp grains that abrade and eventually break the remains apart before they settle on the bottom and are covered. The fragments of shells that wash up on many beaches are the result of this tumbling and abrading action.
Heat
Even if the bones are rapidly buried with sediment, such as when a volcanic eruption sends up large quantities of ash that fall to the ground, it doesn't guarantee permanent fossilization. The Earth's crust is subject to tremendous forces of heat and pressure. Heat from below may reach the rock layer in which the fossil is encased, partially melting the rock and destroying the fossil.
Movement of the Earth's Crust
Anyone who has visited the Grand Canyon in Arizona can attest that exposed rock strata don't necessarily appear as uniformly horizontal layers. They can appear twisted and folded into unusual angles, the result of the Earth's crust slowly moving under enormous pressure for long periods of time. This process can eventually allow the rock layer containing the fossil to move up to the surface where erosion of the rock by wind and rain exposes the fossil -- where it can be found by a paleontologist or amateur fossil hunter. But these high-pressure conditions can also cause the fossil to be flattened and destroyed.