I read a short story about a guy with anterograde amnesia (i.e. being unable to form new memories, as in the film "Memento" or a case described in one of the chapters in the 1985 book The Man Who Mistook His Wife for a Hat by Dr. Oliver Sacks). I don't recall how he got the condition, but I think, in contrast to real-life anterograde amnesia, the guy in this story experienced each day from beginning to end. I think there was a neuroscience researcher, I believe female, who devotes herself to working on a cure for it. At the end, some cure procedure is attempted, but it doesn't work right -- it feels like a thousands of himself (one from each day) are being shoved together. There's some mention by the researcher, toward the end, of how studying him has given science revolutionary insight into the human brain.
This would have been published before "Memento" (2000). Possibly decades before.
I was reminded of this story by a story ID that was resolved as being "Invariant" (1944) by John R. Pierce, but it isn't that one.