If he's in his hide I'd probably wait until the next feeding day and up the ante then, if he's out on the prowl then there's no harm in throwing him another.

Funny you say he's striking from the branch. My room mate's buddy came up from Florida for a few days, turns out he has a BP as well. He housed it with his RTB...bad idea, I know, said Red Tail went off feed about a month after the BP came in and died from starvation. But, he also said that his HP spent a lot of time on the branch, and always hunted from it (striking from above and pulling it up to him like a GTP). Found that kinda cool.