The only times I have had seahorses regurgitate food was after they have overeaten. This is quite uncommon and the occasions I have observed it were always when the seahorses were binging on live foods.
For example, I once had a male reidi in a mixed community tank that couldn’t or wouldn’t stop hunting as long as live prey was still available. When a netful of live brine shrimp was added to the aquarium, he would gorge himself and then continue to chase down nearby shrimp even though he couldn’t swallow another bite. Once filled to capacity, he would slurp up the shrimp as usual, but then immediately spit out the mangled Artemia again and move on to his next victim. He couldn’t resist hunting and striking at the live shrimp, even after he was stuffed to the gills, but at that point he wouldn’t actually ingest the food once he’d killed it. What was it that my Mom always used to tell me in situations like that? "Your eyes are bigger than your stomach," I think. It’s the same with seahorses.
So it’s possible that your male and female have been overeating. You might try reducing the number of frozen Mysis you are offering them at each meal in order to curb this behavior.
The other possibility is that you could have gotten ahold of some bad Mysis that has spoiled. This can happen when a block of frozen Mysis thaws and is then refrozen. If it is not shipped on dry ice, this can occur en route when the frozen Mysis is shipped to the consumer. If the problem persists, consider replacing your frozen Mysis with a fresh supply.
Best of luck with your new seahorses, Haynes! Here’s hoping your female continues eating well and keeps her food down.