You don't have to take a mission immediately. There's a brief window of game time where you might be able to wait for a vital research to complete or for an important soldier to finish a medical procedure without losing the opportunity to go on the mission (and without suffering the consequences of ignoring it).
Unfortunately, I haven't found a table of the mission availability times anywhere, and I never bothered to time it.
I have my first MEC trooper about to finish augmentation in 4 hours, and an abduction mission right now. This is month 2, Enemy Within, Classic Ironman. Can I wait 4 hours for that crucial rocket-punching, fire-drawing, closest-enemy-aim-debuffing MEC, or do I have to take the risk with what I have?
- More generally, how long do I get to wait for any mission?
- Does it depend on difficulty or mission type?
- Is there a randomized component, or is it deterministic?