I'd be checking for notches, scratches or burrs at the saddles and making sure you seat the string properly when stringing it.
What gauge are they?
I haven't broken a string in 20 years despite doing 2 stop bends regularly.
Give the frets a gentle polish if it breaks over a set range of frets. Could be friction wear on the thinnest string. If it breaks up by the nut or any other part then check for burrs. Very light sanding, or (preferably if its gold hardware or expensive) some old, clean cotton rag rubbed over the area should fix that.
I had three A strings break while jamming with my band over the course of a month, one from a set of brand new strings. I too would love to know what the hell I'm doing to the A string that makes it give up and die.
There is a ton of variables and while the problem may be related to where you see a string break, it might also be something completely different.
Have you tried different string brands? One thing that might matter is how you string the guitars. Are you creating twists or kinks and how evenly you stretch the string. Might be worth watching some videos about it. We all forget things even if we've learned them once and there are worse and better methods.
Just two breaks is still mostly just coincidence. Especially on two different guitars. And strings break. Especially top e.
Buddy of mine from way back in the day was a bend master. If he didn't break the high E string on at least one guitar at a show, he wasn't playing his best.