Linda,

We rely on the Company bi-monthly rolls for the bulk of the information on a man’s service. Unfortunately, many of these never survived to be incorporated in the Compiled Service Records developed by the U. S. Army War Department and held at the National Archives.

If a man was transferred, died, deserted, he would be dropped from the rolls once it was ascertained his status. Thereafter, his name would no longer be recorded on the rolls. If he was captured or declared missing, his name would remain on the rolls identified as such.

In the case of your R. H. Middleton, there are 4 missing bi-monthly rolls missing subsequent to his last presence. Whatever happened to him in the 7 month intervening period, he was dropped from the rolls prior to March/April, 1863 for some unknown reason. As such, his name would not later reappear unless he returned which is not the case here.

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It appears there were a number of desertions from his company, see:

http://www.history-sites.com/cgi-bin/bbs62x/arcwmb/arch_config.pl?md=read;id=3361

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There may be some information in this book:

A Courage and Desperation Rarely Equaled: The 36th Arkansas Infantry Regiment
http://www.amazon.com/Courage-Desperation-Rarely-Equaled-Confederate-ebook/dp/B00DQW66MA