I think AhMyGamer is right.
Lightning archer ranks up at Sphere Level 4
Combat monks ranks up at Sphere Level 5
Brave soldier ranks up at Sphere Level 9
So what I think happened was, you had Combat monk and Lightning archer in the field, and you put SPs into your sphere and Sphere Level became 4, and ranked up your Lightning archer. (and it happened to be at night)
Next round, you put 1 or more SP into Sphere Level, ranking up your Combat monk.
Linnear wrote:I proceeded to play my other Brave Soldier, and it did NOT receive a Rank-Up - until I revived it after it got closed.
This part is confusing...
What do you mean your Brave Soldier received a rank up after it got closed?
Did you happen to put almost all SP into your Sphere Level each turn? If so, you may have manually ranked up Brave soldier (meaning you've increased Sphere Level to 9) when you put him out (or revive) the second time.
If not, write down Battle ID number (it's in the top of the chatbox in the game screen) when this happens again, and let us know!