We all have that one pet...
We either bought them when they were a baby, or we bred pets and they had the cutest baby ever. For me, it's the Griffi babies. Sure, they're majestic when they're older, but when they're babies, Griffis are impossibly adorable.
That's why I suggest a philter, or maybe a magical cookie that will freeze the aging process, to keep pets at that perfect age.
So you think, Well, if we do that, will they stay in the hatchery forever? Or will they move on to the Stables?
I think if a pet is fed the foretold magical cookie they should automatically be moved to the Stables and have to be fed like normal pets. This would help moderate how many magical cookies people buy.
I think this could also help control the un-wanted Sylesti pet population!
Think of how many pets get tossed aside daily because their owner doesn't find them interesting or cute anymore. If more pets have the ability of being sold the foretold magical cookie, it's likely more people would be interested in them. And these pets that ingest the cookie can never grow up to be bred a few times then be malnourished and unloved.
I also suggest that players should have to buy the cookies with diamonds just like the magical pies. Think of it. We could boost the economy of Sylestia all over again. Babies that have been fed magical cookies could wind up selling for millions in auctions. They'll be rare, because the original owner of the pet actually had to use diamonds.

Please consider my idea Fai & Krin :)

I think this has already been suggested, somewhere.




Edit
Yep here http://www.sylestia.com/forums/?thread=8135