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That depends on the offense. For many offenses, there is a 5 year statute of limitations in the UCMJ, so for a court martial there would be a 5 year statute of limitations. However, for other offenses, there is no statute of limitations at all. So again, it depends on the offense. Things like murder or sexual assault have no statute of limitations, while theft does.
Improper conduct doesn't really mean anything to me, because it is not an actual crime. Many things could fit into that term.
If the improper conduct was sexual assault, rape, murder, child molestation, kidnapping or if the person has been AWOL the entire time (that time doesn't count against the Statute of Limitations).
Now, whether or not the military would actually charge someone depends on who finds out about the issue and whether or not that person wants to go through the trouble getting the approval to bring the person back on orders. It is not common at all...in fact, it is very rarely done.