If that same level 5 Paladin is consistently hit for high amounts of damage above what the temp HP grants, they will quickly drop. Even moreso if they are hit for a massive single crit or large pool of damage that overwhelms the HP pool entirely.
This is why I say if you're having to spam it, you're likely about to die anyway (which was exactly the scenario described in the initial post, including outcome). You die a little too slowly for impatient wizards
I think the argument can be made, however, it's still a bit strong because of being able to re-use it so rapidly, regardless of the PC's current state. I mean, I don't see it as grossly over-powered in that it doesn't allow you to do anything to your opponent. Yet people have been comparing it to heal, for example, and the latter provokes attacks of opportunity (I think the potion does too) and can't be used when immobile. In comparison to Divine Might and Divine Shield, Divine Vigor requires less investment to obtain it (no strength minimum, no need to take Power Attack). It also auto-scales with level, whereas the other two do not.
It's a new feat, so it's easier for me to believe it needs adjusting than feats that have been around a long, long time...long enough for them to become the bread and butter of certain classes and builds.
ETA: Also, regarding making each a full action, in the case of Divine Vigor, that's less of a penalty because it can have a much, much longer duration.