Don't know if 45 potency per 3s on dots is something really notable to fret over...but for now, yeah, it would be nice to have Iron Jaws simply extend the duration rather than refresh.

It feels like they're preparing to remove dots entirely, since they no longer have any functionality or interaction with the rest of BRD's kit.
An idea: Maybe make them something like the Flare buff for BLM; you only need to apply them once, and they'll continue doing damage so long as you're actively in any song. No refreshing needed.