I've been training and walking my eevee around the map but when I came to check with it I found out it went from believing in me to "neither loves nor hates you"! I came to check if it was the same female eevee I had before, I then realized it was the same one. It didn't even faint at all.
Well, the friendship checker gives the former phrase when a Pokemon's happiness is between 150-199 and it gives the latter at 100-149. It could have only gone down a point or two in between those two checks, which is forgivable. It probably did faint but regardless of whether it did or not (I assume you didn't give it any herbs), just continue loving it and it'll start "believe[ing] in you" very soon!
Hope I helped. :)