I was breeding some Irish Cobs to catelogue the colors, and the "Breed With This Stallion" and "Put Up For Stud" buttons kept disappearing from my boys after using them a few times--somewhere between 2 and 6 times. Putting one up for public stud fixed him, and another one had the button come back after refreshing, but for a third boy the button is still gone.
The studs I have had this glitch on so far:
https://beta-v1.horsereality.com/horses/3672226/f7eb3bf31weeb1845b0z -- Button was gone, came back on refresh, disappeared again and now is still gone
https://beta-v1.horsereality.com/horses/3672389/59d093495w5f41d2815d -- his button disappeared, I added him as a public stud via the Market interface and now it seems to be back for good.