I do believe that is impossible to copy a pet, either they are not in the kiosk anymore, either they are listed and it says they are no longer available. I have tried to copy a pet, then another one, and so on. First 5-6 times I said it is bad luck. Can you please fix the kiosk?
This only seems to happen to me whenever I search for a specific talent, but whenever I just look through available pets of a specific breed or search by pedigree I don't seem to have this issue. My theory (which could very well be incorrect) is that the search function displays all pets with those talents, regardless of whether they're actually available. So if the pet has been recently hatched with and is still in the cooldown period, it would still show up in the search function. It's certainly an issue and needs to be fixed, but at least that might help explain why it's happening?
Pets that are offered through the kiosk have some limitations on hatching.
First, as soon as you hatch with a pet in the kiosk, that pet goes 'out of service' for one hour. No one else can hatch with it and you won't be able to find it again during that hour. If you were thinking about hatching with a particular pet and then suddenly find it's not available, it's possible that someone else hatched with it. Now you would have to wait one hour and search for it again.
(So that's my first bit of advice. If the pet you wanted suddenly seems to disappear, check the time and come back in one hour. It might become available again.)
Second, pets in the kiosk can only hatch a total of ten times. After the tenth hatch, they are taken out of service. Their owner has to come back, take the pet out and then offer it again before it becomes available for hatching again.
The hatching kiosk is set up this way so that more pets go through rotation and get a chance to be hatched with. It would be nice if we could put a 'bookmark' on a pet that interests us. Then, whenever that pet is available, we could find it listed in a special section. Even if the pet is temporarily out, we could see it shaded in the bookmarked tab as offline, out of service, whatever. And maybe the pet owner could get a bonus if someone bookmarked their pet. (What do you say, KingsIsle - maybe you could work that into a future update?)
Alia Misthaven