It may be a matter of guage. And I have noted that this is at the saddle and not at the peg, nut, string tree (if any) or machine head, or anywhere in between. Once you go below standard lights (that might be about a 21 thou G string) they are just a bit small to be tough.

However I'd wonder if it might be the breakover angle, or playing witha flatpick too close to the saddle.

Does it happen with all types of string?