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.