Statute of Limitations, Sgt. Jenkins, and fleeing the country

Or never being in the country in the first place.

Under U.S. law, if you leave the country (or the boundaries of US authority, for military personnel stationed overseas) after committing a crime (a federal crime, in this case), does the statute of limitations still apply?

I ask because currently there’s an awkward situation going on between Japan, N. Korea and the U.S. Last year, five people who’d been kidnapped by N. Korea in the 70’s were returned to Japan. One of them, Hitomi Soga, got married while she was in N. Korea to Sgt. Richard Jenkins, an American who deserted from the Army (I believe. One of the armed forces, anyway) in 1965. The sticky situation is that Soga wants to be with her husband again, the Japanese government is refusing to let her return and is pressuing Pyongyang to let her husband leave, but the U.S. State Department has said that they’ll arrest Jenkins for desertion the second they’re able to.

Now, I’ve heard (and if this is inaccurate, please correct me) that the SoL for this particular crime is 40 years, which would set Jenkins’ expiration date at 2005, not too far in the future. When I brought up this point in an argument, though, I was told that the SoL doesn’t apply if you leave the US, so he’s eligible for arrest no matter how long he waits. This is the case for Japanese law, so it seems plausible that it could be the same for America.

Is it?