During a fight, my team's morale seems to fluctuate a lot. The game said keeping it high is good, though I've forgotten why.
What events cause morale to go up or down? Is there any way I can control it?
Keeping your morale high is very important in most battles against stronger enemies, especially against bosses.
What affects morale boosts and drops:
You get morale boost when you kill enemy units, when you succefully deadlock or flank them, basically whenever you get strategic advantage on the field. The same rule applies to the enemies, if they are stronger then you they will have higher morale at start. Whenever enemies get advantage over you their morale will increase. Some Psionic arts will also increase your morale, such as Addle, Cheer and Dispirit.
What does morale do:
To keep morale up try to keep as many groups as possible. Provided that they must be strong. Also, try to do flank attacks more.