If you are using a 'double' surgeons knot, it's weak and will ALWAYS break right at where the line enters the knot. That's the 'stress point' of this knot, and unless you are using heavy line, the double surgeons is not a very strong loop.

What you want when breaking off a snagged fly is for the knot at the FLY to break, not the one on your loop.

Take the time to test your knots...you'll find that if you use a strong tippet to fly knot, something like a palomar or fisherman's bend, the surgeons knots (ALL of them) will break before the tippet/fly connection does.

What you need is a stronger loop knot, or a way to replace that 'loop to loop' connection with something stronger. The Bimini Twist is about the best, but many find it tiresome or tricky to tie. I've gone to a small metal ring tied in with Palomars (strongest connection I've found so far).

Some research will find you lots of loops...but don't use the Duncan, it's fine for heay butt sections but is too weak for tippet.

Buddy