That's what occured to me, too, when I saw the pics. The leading edge of the saddle looks to have a relatively sharp--not an edge, per se, but a change of aspect between horizontal and vertical. It doesn't look like there's a burr there, but rather that the top-to-face corner is fairly sharp.
It also looks like the string isn't resting on the bottom of the groove, but rather contacts the groove walls up about 1/4 string diameter on each side.
The drop-away angle of the saddle top also looks like it may be steeper than the actual string angle back to the tailpiece. If so, then the string isn't being supported all the way across the saddle, and instead is resting on the front lip, as mica points out.
From the wear pattern in the saddle, it looks like the string contacts the saddle for about three wraps, then the saddle top begins to fall away from under the string. It also looks like the saddle groove is not quite in alignment to the string; both the first and second pictures show that one wall of the groove is flat while the other is rounded.
I think the main cutting edge pressure point is about 1/4 string diameter up on the front edge of the notch, just about exactly where mica's arrow is. In her picture, you can see about three string windings embossed in the saddle on that side, and a pretty clean fulcrum point at the face.
If that _is_ the break point, it's a little tricky to fix. If you file that point of the groove to round-over the lip, you move the apex of the saddle backwards somewhat. Then you start to introduce saddle rattle possibilities. A _very_ fine needle file should be able to round that front edge over; the idea is to change the groove contour to allow the string to contact the saddle along the entire bottom 1/2 of its diameter, while moving the apex point from the exact edge back no more than about 1 winding width.
Smoothing out the winding embossing will also help a bit. Also, relieving the lateral pressure on the back end of the string, where the saddle groove prevents it from running straight to the tailpiece will also help. Carefully widen the back end of the groove on the screw side of the saddle to relieve the cross-grove tension on the string.
Looking at the string itself supports (to my mind) the idea that the string isn't resting completely on the bottom of the groove. I think there's a pinching action going on between the contact points on each side of front lip that's putting extra pressure on the core. The winding embossing in the saddle also suggests a lot of pinch pressure which, coupled with the extra pressure introduced by the groove-to-tailpiece misalignment, could be what's stressing the core.
Finally, the front edge of the bridge frame looks like it's got some string wear on it, which is odd, as the side view picture indicates there's plenty of clearance.
That side view also shows that the down-angle from the bridge to the tailpiece is not too severe; that shouldn't be causing any problems. Shimming the tailpiece would most likely result in a slightly looser feel on the strings, but probably wouldn't affect the breakage problem.
nic
(Greeting all, btw. I'll swing over to Introductions a bit later and post a howdy over there.)