So someone found an exploit to basically quickly toggle badass points on and off to dip HP immediately below 33%, allowing Krieg to Release the Beast and get free cooldown refill after. Then toggle badass points again to dip HP below 33% and rinse & repeat.
Not infinite in the true sense but still quite neat. This of course assumes two things. One is that you have to have enough badass points invested in max health, and the other is that you aren't already almost dead by the time you exit BXR (in which case you'd just re-activate again anyway). Neat trick to use when you just want to have fun with BXR against light mobs and feel all badass.