Art. 43 of the Uniform Code of Military justice
(a) A person charged with absence without leave or missing movement in time of war, or with any offense punishable by death, may be tried at any time without limitation.
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(c) Periods in which the accused is absent without authority or fleeing from justice shall be excluded in computing the period of limitation prescribed in this section (article).
(d) Periods in which the accused was absent from territory in which the United States has the authority to apprehend him, or in the custody of civil authorities, or in the hands of the enemy, shall be excluded in computing the period of limitation prescribed in this article.
Seems like there is no limitations period. Note that the Supremes have not ruled that a statute of limitations is a necessary component of procedural due process.
However, this guy might be able to weasel some sort of "diminished capacity defense." Doubtful, though.
Note well that those subject to the UCMJ do not have the same Constitutional protections that civilians are afforded. Not exactly somthing that they advertise at recruiting stations.