Mortalbane is a tricky one, but it actually deals damage at every opportunity as worded. The reason is that it does not increase an ability's damage by 2d6, but rather it adds 2d6 damage to an ability when it is used against living nonoutsiders.
An easy way to look at this is with a warlock invocation, "chilling tentacles." It is pretty much the most complicated interaction that exists with mortalbane but beautifully demonstrates this concept:
- Tentacles are created, not summoned. Since the tentacle is created by the spell instead of being a pre-existing summoned creature, the tentacle's damage is increased by 2d6 whenever it attacks because that is when it is used (vs a summoned creature that would not have it's damage increased since the creature would not be created by the ability, but rather the transportation of the creature from its origin to its target, which is non-damaging)
- Whenever someone enters the area of this ability, they take additional damage from the cold aura. This aura will also deal an extra 2d6 cold damage from mortalbane per tick.
Imagine that a creature leaves the area of chilling tentacles and then re-enters it. Certainly, both the aura and the tentacles are being used against that creature again. Now from the ability's perspective, staying in the area or leaving/coming back are identical. The important thing is that it's the use of the ability to deal damage that matters, not the activating of the ability in the first place. A single ability that is use multiple times to deal damage will get much greater benefit from mortalbane than an ability that deals damage all-at-once.
That said, house rules are always the winners. If the dm wants to change mortalbane to "deal an extra 2d6 damage the first time it is used against a living nonoutsider," I wouldn't argue.
Link to my previous question on this same topic.
I wanted to add one more thought experiment just to evidence that the damage bonus (or penalty) is applied multiple times. If you have an undead creature being damaged by a mortalbane ability, and after taking half damage, the undead is affected by polymorph any object and turned into a living creature, the next application of damage (i.e. the next time the ability "is used against a living nonoutsider"), then it will take full damage plus 2d6 bonus damage.
Likewise, if a living creature was polymorphed to be non-living or an outsider, it would stop taking bonus damage and instead start taking half damage.