US navy is much stronger than any navy in the world. A long war with a minor power, or a limited war with a major power is not going to cause meaningful casualties to US navy and it's not going to result in a Navy that's significantly shorter in personnel.

A significant war capable of significant damage to the navy as a whole (as opposed to a lucky strike on some ship) essentially requires an open, high stakes war with a nuclear power; and due to MAD such a war can't really be long - if the problem is so irreconilable that it escalates to large scale open hostilities with significant casualties, then that also escalates to nukes, and then it'll be over in a single day.