What do you mean by dropping stitches? Is the needle going down, but not making a stitch? Or is the stitch just longer than the other stitches? In the first case it would not be the BSR, but more likely the needle flexing so that the stitch isn't formed. In that case a larger needle (that wouldn't flex as much) might help. Also slowing down so that the fabric doesn't move (and therefore flex the needle) while the needle is down would help. Or it could be lint in the bobbin case, or probably several other things, but not the BSR. On the other hand, if you're getting long stitches without the needle going down, it could be that the BSR isn't reading the movement of the fabric correctly - or it could be that you're moving the fabric faster than the BSR can keep up with. There's an annoying sound that the Bernina makes when you're moving the fabric too fast, but it's possible that you have that sound turned off. If you don't hear it at all, ever, check your manual and turn it back on. It's annoying, but it does provide useful information.
I haven't used my BSR since I got a longarm, but when I took my Bernina in for servicing I learned that the BSR should also be taken in, so that software updates could be made. This was years ago, but after the first update my BSR started doing a better job than it had previously. So it might be good to find out if your BSR needs software updates.