Asparagus can be one of the more expensive produce items so it would be a shame to let it start wilting before you have a chance to use it.
While fresher is always better, if you can't use your asparagus right away, you can extend its useful life with proper storage.
When storing in the refrigerator, place the asparagus in a glass or wide-mouth jar with approximately two inches of water. This will keep the spears from wilting. A plastic bag (such as those found in the produce section) covering the spears and the jar opening will keep the moisture from evaporating.