Memory is stored as a series of chemical changes or connections in the Brain. So the memory is in fact a neurological matter existing physically in the brain.
Amnesia is loss of memory. The memory can be either wholly or partially lost due to the extent of damage that was caused. There are two main types of amnesia: retrograde amnesia and anterograde amnesia. Retrograde amnesia is the inability to retrieve information that was acquired before a particular date, usually the date of an accident or operation. In some cases the memory loss can extend back decades, while in others the person may lose only a few months of memory. Anterograde amnesia is the inability to transfer new information from the short-term store into the long-term store. People with this type of amnesia cannot remember things for long periods of time
When the bullet pierced Wolverine's admantium skull and penetrated his brain, there was some loss of brain matter. Now either of these two things must have happened -
- When the bullet pierced his brain, it damaged tissue. While his body healed that back, the chemical responses (memories) stored in the tissue were lost indefinitely. So although his brain healed back, and other functions were generated normally - like speaking and walking and so on, the long term memory area suffered significant damage.
- When the bullet pierced his brain, it cut through brain tissue and got lodged somewhere in his brain. So while the other tissues healed back up, body functions and actions were resumed, the part where the bullet was lodged might have been the area where long term memories are stored. So that is the reason his memories might never have reformed. I'm sure what to answer if the bullet was removed and whether the memories would reform.
Personally I'm inclined to agree more with point 1 than 2. Because Professor X can still access some memories in Logan's mind. So I'm thinking damage to the brain with long-term memory affected combined with some degree of Amnesia. This is based on his behavior and occasional remembering some aspects of his previous life.