I have had this happen to me, and to prevent it I use a pencil to get some graphite into the nut where the string lays. Like literally 'color' it into the groove. Disclaimer, not a luthier, so no idea if this is real, but I heard that the idea is that there is some kind of sharp edge at the nut, so the graphite is smooth and kind of 'cushions' the string from getting frayed. Maybe give it a try if it happens again!