I was one of those people that used my Super Smash Bros Link Amiibo to get Epona as soon as I could. Unfortunately, I didn’t realise at the time that this was a rare occurrence and let her run away.
Well, finally, I’m able to stop crying as it appears that whilst it is rare, that you are able to in-fact spawn her a second time using the same Amiibo. It isn’t clear just how often she will spawn, but Press Star team member, James has confirmed that you are able to spawn her twice. People on Reddit are echoing the same sentiment.
As soon as you get her a first (or second) time, you should immediately take her to the nearest stable to register her. You’ll have to pay 20 rupees for a saddle and you won’t be able to name her, she’ll be instantly recognised as Epona, the almighty.
Epona is unique as she has maxed out stats including Strength, Speed, Stamina, Max Bond and a Gentle Temperament.