There is a simple difference between the modern perspective of memory and the Buddhist perspective of memory.
So what is it?
In the modern understanding the brain is the storage device of the mind ("Mind" being a neurological phenomenon).
So to science it is a "As long as a being live" story,so their understanding fits the currently accepted version of scientific truth. Because as to them a creature grows it's brain with age,use it while it is alive and the memories die with the death of the creature.
Science will no longer proceed to a new theory because they have cemented their version of truth with this "only biological understanding!"
So what is the less explained Buddhist perspective?
As Buddhists we do not believe in a "Soul",Now this brings a lot of riddles on to the table because in any other religion "Soul" is like a "Log Book" so for them it is end of story!
If you try to find an answer from already existing sources of Buddhism you will see a certain paradox. Which is nothing else but the complete ignoring of the biological side of this story.
The double paradoxes
If you take a look at the Scientific perspective you will see the exact opposite version of this paradox. Which is the complete ignoring of the Mental side of this story.
- How some people recall past lives
As Buddhism teaches experiences are collected from the senses and stored in "Vinyana" (We need to translate this as "Memory").
This "Vinyana" seems to be the word used for both MIND and MEMORY,like it is a combination of those two.
We know different parts of the brain work with different senses of the body.and this spark a lot of neurological activities (I belive this are the "Sith or thoughts").so for sceince this is only brain activity but to Buddhism this is the mind being created by events,thought and logic.
The simple thing you must understand is,The scientific theory of mind is based on how brain works,But Buddhism theory of mind is what fuels the brain activity and how to make it controllable.Because normal chaotic brain activity is not Buddhism way of a perfect mind.This are the "Duel Paradoxes".
Memories of a Previous Life:
Brains of Buddhist monks scanned in meditation study
buddhist monk displays unheard of brain activity while meditating
This Vinyana seems to be quite like a computers memory.
Imagine it this way...
If you copy files from your computer to your phone you can still see them working the same way,
just like the memories of a person.
As Buddhism says in the moment of death a beings mind creates a backup copy of itself which will take residence in the next life this creature is about to live.So this is how the information about memories travel.this is not one set of memories traveling it is a copy of the original set of memories from the being.
As for how some are able to recall,it is not explained in Buddhism but if someone do a good karma and wish for it then it will happen,but there is no other way explained in records.
[Please refer "Abhidhamma" for more details]
So how does the memory works?
Memories are not actually real - buddhist view of memories
Memories are collected details reconstructed by the brain.So the senses of a body gather data (vibrations,light) and the vinyanas dedicated to those senses create the image or the sound and etc.,this is then collected by the "Mano vinyana" to create thought and logic.These are then stored as memories.As to new discoveries there is a dedicated neurological highway to each and every memory,So what a memory is nothing but a brain's unique and dedicated neurological path.The so called "Vinyana" is the collection of neurological pulses that occur and disappear each millisecond .In the end Science and Buddhism are two parallel subjects with different viewpoints.
"Quick lesson in Abhidhamma"
If you have any questions regarding my answer please ask in the comments section below.