If your soldier gets gravely wounded in a mission, there is a chance that the soldier gets shaken. This chance is 20/25/25/30% for the four difficulties.
What is gravely wounded? It means that the recovery time is more than 168 Hours (336 on Legendary) - this is determined at the end of the mission.
How is recovery time determined? Based on the lowest HP percentage at any point in the mission, a number is generated within certain limits. There are four "buckets": up to 20%, 21-50%, 51-75%, 76+%.
Example, your Soldier has 10 HP and takes 6 Damage, which brings him down to 40% health. At the end of the mission, the game looks in the 21-50% bucket to see the range of how long recovery takes and picks a random number from that. If that random number is more than 168 hours (336 on legendary), you're gravely wounded and the game rolls if you're shaken.
Note that the source of damage doesn't play into it, and neither does healing. The game records the lowest your HP ever was. E.g., 10 health, take 6 damage, heal 4 damage, take 3 more damage, heal 4 damage -> Even though you end the mission with 9 HP, the game records that you were down to 4 HP, which is 40% of 10. That percentage is the ONLY thing that counts.
I do note that the spread between best and worst recover time is MASSIVE. For example, a single point of damage (the 76%+ bucket) on Rookie difficulty puts your Soldier out of commission for 5 to 25 days - completely random.
For more technical details, I dug into the source code here.
Bonus Answer: If you recover from being shaken, you get a permanent increase to Will (4 to 13 points) and can't be shaken again - it's like Vaccination.
Best Answer
I have seen the following bugs at the mission prep screen during my playthrough:
The Make X available buttons overlap. Sometimes the buttons does not displayed at the correct position and instead they are overlapping each other.
Functionality switch-up. Sometimes the Make armor Available button makes the Utility items available, or vica-versa. Thankfully the Alarm message before the action states correctly what are you trying to remove.
Make X available doesn't makes some of the equipment available on not selected soldiers.
Make X available removes equipment from selected soldiers. I have only seen this very few times but it happened to me too.
Frankly those buttons are bugged to hell, I would advice that instead of relying on them just manage your items manually. You can switch in healthy soldiers to remove their equipment, or you can just escape from the mission prep screen and manage the inventory in the Armory / Soldiers screen.