Sometimes when I capture a pet it doesn't show up in my stables or hatchery. I know that I captured it because my trap is gone and it says that I ganed no experence.

When that happens, the pet actually runs away. You can read the battle log to see whether you caught it or it ran away. If you caught it, it will provide a link to your new pet's profile. If it ran away, it will say it ran away.

Thanks!!!