I'd have to agree with the others as far as I've never had an eye bite or cut through my line.....and I always use 6-10 lb mono on homeade worm harnesses. I would also suspect that possibly the knot, and/or wetting the line when cinching down your knot could be the culprit. You would be
surprised how monofilament line can heat/thin, and become weakened
by just pulling knots tight when cinching them down without wetting them
Also....is the line actually breaking, or is the knot pulling through itself?
If the line is pulling through itself...you might consider tying that particular knot with a couple extra wraps before cinching it tight or...perhaps tying a different type of knot.
Is your line "curly" at the end with no hook? If so, then you probably need
to tie with more wraps around the main line, or use a different type of knot.
Is your line "broke" with more of a clean break of your line at the end? If this is the case, it could be your knot tie, or possibly even old, weakened
line. Keep in mind....if using monofilament line, that mono absorbs water,
and eventually becomes weakened with UV rays and repeated exposure
to sunlight and moisture.
Hope these tips give you some insight and ideas as to what may be happening.