'Deserted by not keeping up with' and 'certificate' are two different notations. For one reason or another men might drop of out line during a march. Envision a long column of tired men stumbling down a road on a rainy night. In these conditions officers couldn't track which men had dropped out where during the night, only knowing that some didn't answer the next roll. Each soldier was expected to catch up or keep up ASAP. Anyone who failed to do so in a reasonable time or showing up without a reasonable excuse was considered a deserter.
'Certificate' can only mean a surgeon's certificate. I don't know why the orderly sergeant made that notation except that perhaps a cerificate was expected on this man due to past health issues. A furlough issued under General Earl Van Dorn's authority surfaced later, the date on it being Oct. 20th.
This soldier seems to have been absent at home or otherwise away from his command for the remainder of the war. Oftentimes a man who had been absent for such an extended period would have been dropped from the roll. For whatever reason, this man wasn't. The date Feb. 29th 1865 covers the last period on roll. Because he was absent no one in the company could know whether this man was dead or alive. The date is a roll date -- nothing more.
Locating anything addition from the wartime period would be extremely difficult. I can't imagine where you should look for other material that might reward your efforts.