I was under the impression that you only get recovery quests when you have agents incapacitated. However, even with some out of action right now, I have yet to see a recovery task pop up. It's a safe bet that it's simply not working as intended.
There's a screenshot of a guy with max in all quest types, even recovery. So I guess they do exist, but I have never gotten one either. And I have a bunch of incapacitated agents on 7 accounts all the time.
Apparently you can retire uncommon+ agents and pick recovery experience. That looks to be the only way to get it at this time. Not sure if that's by design or not.
I ended up with a second emperor crush. and you can only make use of one elite of the same dude at any given time. so I retired mine. got from base xp, to 95% towards level 5 with one dude.
I'm missing a few uncommon agents myself after sending them out along with the missing mission. Still watching for them to rotate back in. With no log each time or outputfile it gets hard to keep track of after a while.