I think you just need to strengthen your core. Not only do back handsprings but always do the drills given too. What I have notices is inconsistent back handsprings become more consistent with drills - such as jump back drills (jump on the crash mat), hand stand pops (when you do a hand stand, shrug your shoulders and try and jump), back- walkovers or even back bend kick overs, back extension rolls, handstand forward rolls, even doing a few on a cheese mat (wedge) in between. All of this will strengthen your core and use the muscles that you need for handsprings. Also, your body will "remember" positions and it's almost a memory in motion thing where you don't even need to think anymore, it just happens!
My squad hates drills but those who do their drills and properly are the ones who end up with the better most consistent handsprings :-)