Wonderful Pet Owner Medal Glitch?

Argh. That's sad to hear.
My snail has 4hr. 20min. remaining (cuz I did not know the secret trick) and has 400 or so closeness. So it's totally possible...

 Top Secret

If you release your snail for less than 1 minute, the timer won't go down. So keep putting the snail back to inventory and release again, and the snail will never expire.