The Constitution doesn't really provide strings for withdrawing that power, although they can certainly cut off the budget for the soldiers.
But, yes, they MUST pass that power to the President. It's required. Even the Founding Fathers knew that Congress couldn't run a war.
The Constitution says nothing about passing a resolution, it is not obviously in keeping with the Constitution, since the word is nowhere to be found.
In my view, Article 1 Sectino 8 of the Constitution was a way to throw a bone to those who knew they would be future legislators. Its basically saying, "OK, Congress you can have a little input in military matters too." Even though most, if not all military power is given to the President as Commander in Chief of the military.
I like and respect Dr. Paul, but I certainly trust the constitutional wisdom of Adams, Jefferson, and Reagan over his.