There are no missions that become unavailable after a set time. Once a missions is avaialble to do, it will be there until its completed. There are however missions that are only available on certain days of the week, or at certain times of the day. These will appear the specified day or time, last for a set time, and then become unavailable again until the day or time comes around again. As long as you don't complete them the missions will re-appear again on the set day or time until you do so.
"You know what time it is? It's clobberin' time..." "Look who just sprayed ya with a can o' whooppass"