I've had two of the Garmin Premium Soft Straps in the last nine years. They've worked great for me. I just rinse it off under running water immediately after a ride. Just got my second strap maybe two years or less ago. I seem to remember my first was starting to act like you described and even with battery change it didn't help.
You can find the Garmin Premium Soft Straps online for less than fifty bucks. Though some people have issues with them, I think mine have been solid. I wonder if it's those that sweat so much salt that they crust up their clothes, strap and anything else that have the real crazy issues and low success with the Garmin strap. I'm fairly low salt on my diet compared to others.