Common Reasons Strings Break
If the string slots in the bridge or top nut are too narrow, the strings will not slide through them during tuning. This can cause strings to break.
The notches are too small for the strings (exaggerated for demonstration purpose)
The notches are correct
As mentioned previously, applying a small amount of graphite from a soft pencil to the bridge and top nut notches allows the strings to slide more easily and last longer.
The notches are darkened with a soft pencil
If the slots in the tailpiece are too narrow, strings cannot be pulled all the way through so that the ball on the end of the string seats into position. This can cause strings to break.
The slot is too narrow for the string to pull through
When a string is pinched against the side of the pegbox,the friction can break the string, or worse, crack the pegbox.
The string should not be pinched against the wall (in the above picture, the violin's D-string is undesirably pinched against the wall)
Strings can also become squeezed between the peg and the bottom of the pegbox, especially where a string is doubled on the peg. This not only can cause the string to break, but can also damage the peg and the hole in the pegbox.
Insufficient space for the string between peg and bottom of pegbox
If the top nut does not have the correct curve, it can force the string to bend at a sharp angle on either side of the topnut. This stresses the string and it can break.
Top nut too angled
Topnut too flat
Correctly shaped topnut
Some fine tuners have sharp edges that cause E strings with looped ends to break. A violin maker can round off these edges.
On the left: Sharp square edge
When tuning your instrument, try not to go above the correct pitch of the string as this will stress the string, making it break sooner.