If his decisions were any indication, Chase believed that Davis had always been a citizen of the US.
However, he may have believed that being stripped of his right to vote by the 14th Amendment may have constituted a punishment to Davis and that further punishment would be double jeopardy. That's one theory.
Political considerations, though, were probably the most important reason why the case didn't go forward.
Here is more from a different source. NOT the Salmon P Chase source.
http://www.encyclopediavirginia.org/jefferson_davis_s_imprisonment#start_entry
You say that as if things changed.