You can within the parameters set by the mission designer. If the mission is set to end after, for example, fifteen minutes, then it will end whether you want it to or not.
If the mission is more open ended, i.e. it ends when objective X is accomplished, then it ends at that time whenever that is.
Finally you can have missions that have no end and they'll just continue. Obviously that wouldn't work too well after all planes are shot down so you as the host always have the ability to end a given mission.
But in any case you can set up your session (not the mission but the hosting session) to run missions continuously in a loop. And, even if you have just one session running, the game will automatically re-run that same mission when the first one is ended.
WH_JoeBob
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I'm a Chickenhawk and you're my victim, ya gonna come along quiet or do I gotta muss ya up?