Everything ive read says that the Suzukis with automatic tranny have to be started after every 2 hours of towing & run through the gears. is yours an automatic ? if so do you do this ?
We towed two Chevy Trackers (a Suzuki Vitara with a bow-tie emblem) for over 60k miles, all across the USA and Canada. Always ran the engine a couple minutes somewhere around 200 miles, give or take, whenever we stopped for a break around that time. I would take a potty break and refill my beverage and my wife would hop out and start the car. All done in about 5-8 minutes total.
Always ignored the 55 mph towing speed limit, though.
I know people who did neither thing, and others who religiously did both. All of our Suzukis & Trackers performed just fine and had long and useful lives.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL