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Department of Veteran Affairs spokesman Phil Budahn says the VA last checked in on the benefits recipients in the fall. Both were alive, but in poor health.
Budahn says it's likely that the children of the Civil War veterans, who have wished to remain anonymous, both had illnesses that prevented them from ever becoming self-sufficient..
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As of 2007 there were also 50 Spanish-American War veterans widows and 62 children receiving benefits, and over 2,000 widows and over 2000 children of WWI veterans on the rolls. Source
Since 1958, Confederate veterans have been considered US veterans (even though there were only at most one or two left by that date and they may not have been authentic). I don't know how exactly that would affect the children of rebel veterans.
Very interesting information.