You have to be actively striking (at) the mob to keep it claimed in this manner, spells etc SHOULD keep it claimed as long as you do not die and have performed several hate getting actions against the mob or on players that have performed hate getting actions on the mobs (cures/buffs etc), i have held several NMs as whm curing myself to let the rest of my alliance escape and it has not gone yellow.
I have had the random unclaiming happen to me with the ironclad in abyssea - attohwa(sp?) i pulled him from his spawn point and brought him back to the conflux where my husband and i were killing him, i Nuke him with water 5 for 1800 points of dmg and promptly bio 2 him to get hate off my husband who is on pup using his blm frame. This SHOULD get me stable hate for at least some time even without drawing my weapon because you never draw it to kite the mob. While i pull it around the rock, it is still DoT'ed with bio 2 and helix, it goes yellow. I throw another bio 2 at it like wtf, it goes red, then 5 sec later goes yellow again, the whole time it's still chasing me. So i keep chucking stuff at it, finally it goes down. I have also had similar things happen in ulegrande range on isegebind or whatever it is, he was chasing our rng around, not regening or anything and she still had both her daggers drawn, the mob still had hate on an original member but our procs reset and anyone could have taken him at any time even though we still clearly had viable hate.
I keep thinking of similar situations to this, we were looking for yellow !! on a seal mob, i was tanking it as thf/nin i had done easily 12k+ dmg to the thing with weaponskills so as i was in danger of killing it, i turned around to let the mages do their thing, and while i was still engaged to the mob (daggers drawn) it went yellow, someone could have stolen it out from under us if there had been anyone around. Yes if you fully wipe (we delayed an NM from depopping to help someone that HAD fully wiped) the NM is free for all, but the random unclaims like i stated above are irritating and potentially harmful.