I found in the FAQ an issue, which is odd bc so far know one else has this issue for a character named Asviloka.
thread: http://www.sylestia.com/forums/?thread=13417&page=1#9
for some reason her breeding generator list is not ALWAYS organized, if you look carefully at the screenshot you will find that a pet with a higher id appears under one with a lower ID, and apparently this makes breeding a bit difficult for her.

The old (and currently used) pet table in the database isn't really organized. It causes the entries to become shuffled through various queries.

I don't think I'm having the results ordered for the breeding grounds so it just grabs them from the table in w/e order they're in - which changes quite frequently.

At least, that would be my guess.

When I revamp the generate page, not only will it use a new table that is organized, but I will also probably come up with a better method for selecting pets.

But at this time, there really isn't anything that I can do.