Random Power level Drop

I JUST reached 954 power. The prompt for the urgent quest came up. I go to the location, wait for the acceptance window to open, it opens and I can't join because I'm underpowered. FOR SOME REASON, between town and there, my power level dropped 20 points and missed out on it. No reason for this, and it's not the first time this happened. ANY explaination?

If you have multiple weapons in your weapon pallete, your BP will be different depending on which is currently selected.

@Herr-Tenma Thank you, that makes sense. Noted for when NGS releases!