This has been happening to me for a while, but now I'm a little more attentive as one of my favorite horses died in game, but I am not able to put him in the Memorial Garden I have.
Some horses I am able to put in, while others I am not. I don't really understand why only some show up while others don't.
The horse(s) I'm trying to put in have died last night/this morning, yesterday, a week ago, 2 weeks ago, etc. (I have a lot of older horses who pass away all the time).
Is it possibly because some of these horses are wearing "tack" (ribbons, award blankets, etc.) when they die, and it causes an error in the game? Some horses that have died previously that have no tack, I can click on their name in the mailbox message, and I can view their page. Others just say error, which I think are the ones that are wearing "tack" (ribbons). [I say " "tack" (ribbons) " because the horses are not wearing bridles, saddles, boots, etc., just ribbons and award blankets]
Is there some unwritten rule about which horses are able to be put in Memorial Gardens? Is it an actual game error where horses who wear tack when they die are wiped from the database? Or are there just too many horses in the game and some just get wiped from the database at random to make room without being able to be put into a MG?
I would ask about length of time, "after a horse dies you have to wait x amount of time in order to put them in", but as I stated previously, I have horses die extremely often (multiple times a week sometimes), and that would have already answered my question.
Been on this game for a long time and it seems that there are a lot of unwritten rules/facts about the game, that definitely need to be updated into the current Game Guide.
Taken from the Memorial Garden Section in the Game Guide:
"Memorial Gardens If you have a horses that pass away from old age, you may want to convert one of your empty pastures to a Memorial Garden. Horses that pass away from old age may be added to your garden with a special note of remembrance. It is a nice way to keep your favorite horses around after they die, so they are never forgotten. Horses that are in your garden will not be deleted from the game.It is important to note that Memorial Gardens are permanent additions to your stable. They can't be converted back to pastures or sold. Also, horses that are sent to the Free Range may not be added to your garden, only horses that pass away of old age." 
Hurricane ! Follow Evacuation Routes.
