The archer bosses on fel stop shooting after a certain amount of time. I don't know if this is due to lack of stamina or because their arrows ran out, but this doesn't seem to happen on melee bosses.
Its Arrows, most of them have between 50 - 100 of them and burn through them very fast. In my opinion it isn't an issue with trash/ lesser MoBs but when it comes to specials and boss MoBs its pretty unfortunate. One thing that staff could do for the boss ones is to give them 5k arrows and have the arrows loot type set to blessed so they don't drop upon death and are unlikely to run out during anything but a siege :-P, they could even do this so that their MoBs can use the special arrows without worry that people will farm them for them (Alaric might remember my little friend and his rapid firing ice arrow stick *Giggles*).