I had SuperSU installed, everything was fine, anything I did with the phone worked. After a week it said the SU binaries were missing, and you couldn't get into SuperSU to do anything, but previously you could. If the phone was never rooted correctly like you say, i would have had this problem from the start.
Also after rooting I used a root checker which said I was rooted, but after this Su binary issue started, it said I wasn't rooted.
Still, I'm back to unrooted now, and the only reason I did it was to get Sense 6, which has since come out as an update, so I'm no worse off
Sent from my HTC One using XDA Free mobile app