You can learn about dog foods and how to read labels here:
www.dogfoodanalysis.com

For a start, read a few 6 star reviews and then read a few 2 star reviews. You will catch on quickly!

As already said, Science Diet is not a very good food; the Taste of the Wild mentioned is an excellent choice!

It could be the issue is not his food, but perhaps a treat? Or, being a beagle, something he finds and eats while outdoors? Because you said it seems random with him being fine for a few days to a few weeks at a time

Getting him on a quality food will be a good first step.