If you upgrade both segments on a connecting flight with PlusPoints, United will only charge PlusPoints once, at the same rate as the most expensive segment.

But ... what exactly is a connecting flight?

I recently flew the following route and had to pay PlusPoints twice (=2x20PP):

Tuesday
JAC DEN 6:09pm-7:39pm
Wednesday
DEN LGA 5:35pm-11:16pm

Why did I have to? Or asked another way, how would I have had to fly so that I only had to pay 20PP once?