There was a time in my life when I was impressed by my experiences of deja vu and worked with it to try to outline my most recent past life.  The results were indeterminate and nothing more than frustrating, to the extent that my initial conviction that I was onto something soured.  I don't know and I have to leave it at that, although I must admit I got quite a few clues nothing ever led to anything concrete.

I am pretty sure the center of memory is the physical brain, as we see it destroyed with brain-destroying diseases, and so we have to think the same thing happens when our brain decays at death.  To say we carry some sort of memory to another life, then, would require we posit a second, separate, center of memory that survives our death -- a bit much.  It is plain enough very few if any have access to such memories.

Still, the way our mind seems to be an ongoing process of some sort of unknown phenomena wave providing sentience and sensation and so on would suggest that it is independent of brain and would indeed persist, but at quite a loss when it is stripped of life's memories.  This is similar but not quite the same as traditional Buddhist thought, and quite the same if you take out the superstitious wishful thinking of those who want to turn rebirth into a means for personal immortality, which it ain't.