Once you find the spot, you can catch more. There are like six spots where they show up so once you find where on is you have unlimited feebas

Personally that never happened to me but good lord that would be terrible... I still had a bad experience with one though. Apparently, there was a max amount of berries you could give to a Pokémon and I had no idea. I took all of the berries I could find that gave Feebas beauty to get it to evolve to a Milotic and right when it was about to be maxed out the game told me I couldn't give it anymore berries :'( At some point I got a Ditto in the game so I got more Feebas but I never did manage to get a Milotic... I wanted one ever since I beat The Pike Queen Lucy and saw how awesome it was.