Upgrade your AP production at the start of each battle.

During battle, you can tap little Rumi Aikawa in the bottom-left corner of the screen to increase the speed of your AP gain. The downside is that each subsequent increase costs more and more AP. Still, activating one or more AP upgrades during battle will make a big difference in your ability to overwhelm the enemy with swarms of units.

You want to use Rumi's AP upgrades as much as possible without allowing the first enemy forces to reach your base. The farther the enemy base is from yours, the more AP upgrades you can activate before you have to start summoning units. The sweet spot tends to be two upgrades, but I often go for three. As the battle progresses, you can buy further upgrades if you have sufficient forces on the ground and AP to burn.