Perhaps start by identifying why / how you're losing data.
Check what errors precipitate this, if you're spending too much time in the interrupt handler or callback.
Perhaps move to using DMA to provide you some buffer or elasticity against delays in processing beyond the single byte time that interrupts afford you.
Check relative priorities, and preemption. You really want the quick in-and-out stuff to be able to preempt and stash the data away.
