Quick search by citation:

10 U.S. Code § 671b - Members: service extension when Congress is not in session

Notwithstanding any other provision of law, when the President determines that the national interest so requires, he may, if Congress is not in session, having adjourned sine die, authorize the Secretary of Defense to extend for not more than six months enlistments, appointments, periods of active duty, periods of active duty for training, periods of obligated service, or other military status, in any component of the armed forces, that expire before the thirtieth day after Congress next convenes or reconvenes.
An extension under this section continues until the sixtieth day after Congress next convenes or reconvenes or until the expiration of the period of extension specified by the Secretary of Defense, whichever occurs earlier, unless sooner terminated by law or Executive order.
Editorial Notes

1989—Subsec. (a). Pub. L. 101–189 substituted “armed forces” for “Armed Forces of the United States”.