What to do if I did not register Epona from the Super Smash Brothers Link amiibo at a stable
I'm the one who asked What are the requirements for unlocking Epona?, and I think I may have a solution. I'm posting it here since my question already has a fitting answer, considering how it was worded. Of course my situation wasn't quite the same since Epona did not spawn the first time I used the amiibo, but maybe it'll work for you as well.
As discovered by user SkipReplay in this thread, there seems to be a much higher chance of getting Epona to (re)spawn if you use other amiibos in-between attempts. Just load your save (wait until the next day if you've already tried using the Link amiibo) and go through as many amiibos as you can, then use Link last. Of course you need a couple of other amiibos to do this, but it doesn't seem like the required amount is very high (I scanned 7 other amiibos, fewer than that could be enough as well).
Not sure why this works, but for at least two people (SkipReplay and myself) it worked on the first try.
I was able to get Epona again after she got stuck, and in fact got a second Epona right after. I believe the criteria is that if she exists in the world, she will not appear by using an Amiibo. Try catching and registering a horse, maybe take it out and reboard it before trying again.
My experience was summoning her before finding my first stable. I left her next to a river near the Dueling Peaks as I went after a tower. When I returned some monsters spawned and scared her in to the water. She proceeded to swim towards a small island and would not reenter the water when I tried to steer her to the shore.
Midnight passed and I tried the Amiibo again, which gave the chest and materials like other Zelda Amiibos return. I happened to catch and register a horse before trying the Amiibo a third time, as well as traveling great distances. On day three the Super Smash Bros. Link Amiibo gave me Epona once again, who I registered and boarded immediately.
I dug out my own set of Amiibo that same day, as I had been using my wife's before, and my own SSB Link Amiibo gave me another Epona! After registering her I now have two at the stables.