All new missions start spawning at the start of any new month, in some cases only if a prerequisite research was completed. So you will never miss out new missions (with the sole exception of Save a Sister, which cannot spawn past October 2601), only sometimes they're already too easy, depending on how far in the game you are.
I think I have not seen save a sister.
I think I am slow at playing through. I started with 0.99D only started shooting down craft near the end of the first year.
I am in the second year now and many missions I get are far too easy, especially ratman rodeo but also the academy research, tower and church raid missions. They were all there pretty much from the start and fine then, but now they are no challenge at all and I would take the auto-battle option if there was one. I only do them for the few measly reputation points they give (typically < 100).
Oh, and I would very much prefer if the enemy progression and mission progression was not tied to time. It made some sense for the original game and I did not like it but in the piratez-World there is no alien invasion so it should not matter whether you do the same stuff within a year or five. I simply do not like to be stressed. I would suggest to instead tie this stuff to something the player does, to his reputation perhaps.
That way if you stir up more trouble you get more money, but your enemies get stronger as well. If you keep a low profile your enemies won't notice and stay relatively weak.