When repositioning the frets it is very important to move the frets by applying equal pressure to the edges of the fret and the string across the back of the neck. This will help prevent the strings from breaking. It is unfortunate, but frequently the frets are tied onto the sitars before the shellack has dried on the neck. This often causes the strings to stick at first. Applying gentle pressure is typically all that is needed to free them, but the strings do tend to become brittle as a result of the dried shellack. Fortunately re-tying the frets is not terribly difficult. I will soon be keeping bundles of twine at the shop. In the meantime, however if you find that you need to re-tie a fret and you have no twine drop us a line and i will order some. Fishing line is also a viable substitute, never greater than 20lb test. It may take a couple of purchases to find the right weight line. I have also found it helpful to use tape to secure the fret from the top so that it remains upright while stringing it, allowing you to use both hands to wrap the twine.
The following diagrams illustrate the proper method to re-tie a broken fret.
The color photo was taken from the Ali Akbar college of music website.