Just a few things-
Don't handle a snake that's not eating- at all! Handling puts a snake on the defensive & can hurt what little appetite they have. Snakes (especially shyer ones as BPs are) need to feel they have the "upper hand" so to speak. Nothing says "no control" like being picked up by a "giant".They stop thinking about food when handled, & more about "Am I about to get eaten?" Snakes rely on their instincts to survive, and the only thing that picks up a snake in the wild is a predator about to EAT them.
Don't handle snakes that don't feed well...until they do, & then proceed slowly.
I'll bet the ambient temperatures in your house are cooler this time of year. So when you take your snake out to handle, he's also sensing the cooler temperatures that to him translates to "It's winter, don't eat!" Your warm hands don't make up for a cooler house- you're making it worse by handling him. It's all about instincts again: in the wild, snakes that get caught with food in their belly when it's too cold to digest can get very sick & die from rotting food in their gut. It helps to understand why snakes refuse to eat in winter- you're fighting their deepest instincts.
FYI: Not all illnesses in snakes are RI's- many devastating illnesses can be transferred on re-offered prey. I'm glad to see this is your only snake & re-offering food isn't an issue anyway- it's a bad idea that far too many keepers take chances with, just so you know. Saving a few bucks on a mouse gets very expensive in the long run if you end up needing vet care for a sick snake- let's stick with good advice here, folks?