The cheap strip on Amazon or Ebay are just that, cheap, and not outdoor rated. They might last a year, or forever. A lot depends on where you're located. Maybe forever if your in the SW, maybe a year or two if in the NE.
A company named Recpro on Ebay sells a kit that is IP68 outdoor rated for about $50. The LED strip is encased in a waterproof silicone sleeve. The kit comes with plastic channels you attach to underside of the awning rail with included 3M tape, then the LED strip snaps into this channel. They make it this way as 3m tape will not stick to the silicone sleeve. The bad side is if you cut it to length you compromise the silicone encasement, but its available in different lengths. It is alsobonly sold in white or blue so you can't make the campground look like the Vegas strip of thats your thing.