Glad you liked the game! The full version has been available since May of 2014 here: http://fancyfishgames.com/DeityQuest/ , and in recent news, it just got greenlit so there'll be an updated version on steam soon.

Followers will only stop dealing damage to the opponent if they cannot attack. This is usually because they are Arcane and have run out of mana (if they are Arcane, you'll see a mana bar above the follower), or they are Divine and cannot use your mana (you can set how much of your mana they can use by moving the slider on the big mana bar. Everything to the left of the thumb they can use, but you can only use mana to the right of the thumb for your own spells - so it's a trade-off). You'll regenerate one mana every battle, but if you field a lot of Divine followers, you can often find yourself running out of mana.

My recommendation is to field more Martial followers - they don't need mana for any of their skills and so can always attack (as long as they are in range). Also, if Arcane followers are running out of mana, you can recharge them with grapes or the Recharge spell. Divine followers may be strong (and therefore tempting to field), but having more than one or two will quickly drain your mana. As an aside, some followers (like the Electric Eel) can recharge other arcane followers, so you can use them as a battery to keep your followers fighting longer. The battle system is quite complex, and even though the followers fight by themselves, you can't just sit back and relax, you have to manage them real time :P. There's a pretty in-depth battle guide here: http://www.indiedb.com/games/deity-quest/tutorials/deity-quest-starters-guide , although I bet you don't want to read that!