On my old '11 5.3 w/range installed my I/M monitors would not run the EVAP tests. No CEL on or any codes stored. Only knew it as it wouldn't pass NJ inspection. I finally tracked it down to a bad MAP. It was erratic enough to stop tests running yet not bad enough to trigger any codes. My scan tool has 2 MAP tests, and it was erratically failing one of the tests.
Here's a tip to see if the MAP is fully OK, does the instant mpg go to 99 mpg on a long coast down with your foot off the gas? If not it's bad. I lost 2-3 mpg on a highway run that I have been doing for years, same route always, and that had me searching for issues like brakes dragging and other things trying to figure that out. New MAP got it back to normal 19 mpg.