There are at least 4 billion reasons why your beagle could possibly throw up.
the MOST common i have see is they eat something that they shouldnt have. and they seem to have a natural kick back system that gets it back out.
i have found their vomit with rocks in it, sticks, plastic, paper clips, pieces of stuffed animal, etc.
i think the biggest thing to watch for is.. are they eating? and are they peeing/ pooing.
if either of those stops. there is a problem.
One thing that can help with upset tummies - about a heaping teashpoon of cottage cheese mixed with their kibble - my vet told me about this. The Beaglebratz love cottage cheese so I give it to them 2 - 3 times a week - just for good measure and it gives them a little low-fat treat plus is good for them.