I think I need to replace the headset on my 1989 KHS Montana Summit mountain bike, which uses a 1 inch threaded headset with loose bearings (if memory serves, but they might be caged).

The reason I think I may need to replace it: It works loose after only 200 to 300 miles or so, and yes, it is assembled properly, and the threads are not damaged.

Would it be worth the expense to upgrade to a roller bearing headset as sold by Velo Orange?

The bike is going to be used for everything from around town to long distance self-supported touring both on and off road in all types of weather, including cold, rain, snow, to dust storms and hurricanes when one of the bad weather possibilities hits while I am on the road.

Murphy's Law states in its complete form: "If anything can go wrong, it will; and at the most inopportune time."
And, let us not forget The General's Credo: "Mr. Murphy was an optimist."