Musters were not always held on the last day of the month, it could be days or weeks later.
If that is all that is noted on his CSR cards, that's about as far as you're going to get through that source. He could have died anytime in January or February 29, 1864 which I assume is the date that muster was held.
What was your ggrandfather's name and his unit affiliation?
There is always a possibility another roster of his company may be out there.
George Martin