Does my follower's enchanted weapon need to be refilled?

If I give an enchanted weapon to my follower, will I need to periodically refill it using a soul gem?

If so, is there any indication of when it has been drained, and is there any easy way of refilling it other than taking it, equipping it, refilling and then returning?

Yes followers weapons lose charge when they use them. (source) However some say they they lose charge at a slower rate than normal. (source)

However, I don't believe there is an easier way to recharge the weapon that your follower is using. Looks like you'll have to periodically check it and then take it from them and recharge it and then give it back.

Equip them with items that reduce the cost of the appropriate school (the school governing the enchant) 100% and the weapon will not lose charge. You can do this on a single item with the alchemy/enchanting loop or spread it over 4 items reducing it by 25% each (head, ring, amulet and armor).