I'm so sorry about Buddy

Please don't give up. Spend every minute you can looking online and signing up to every lost/found website. Check the small ads on any news sites. Sign up to any Beagle specific forums and spread the word. Beagle breeders may be approached with a dog for sale and if they kow about Buddy they will be more vigilant.
Can I assue Buddy is chipped? The good news is any vet worth their salt now checks new patients for existing chips and checks against Petlog. Make sure Petlog know he is missing of course.
Local animal shelters need to know he is missing too.
Good luck and please keep us updated. You're living my worst nightmare.