A sitar carries three populations of string with three different jobs, and only one of those is ever pressed to the frets. Sorting them out is the first step to knowing what you actually need to replace.
The playing strings
The main melody string is the one that does nearly all the work: it is fretted, bent across the curved frets, and takes the whole force of the playing technique. It is also the string that wears fastest and breaks most, and any sitarist keeps spares. The other main strings beside it are played much less, and last much longer.
The chikari
The chikari strings are short drones, struck rather than fretted, and they sound the tonic and its octave as punctuation. They are tuned to the raga rather than to a fixed pitch, so their tuning changes with what you are playing — a fact worth knowing before you decide something is out of tune. They break rarely and are quick to replace.
The sympathetic strings
Beneath the frets run a row of thin strings that are never played directly. They are tuned to the swaras of the raga being performed and they ring on their own when the note above them sounds — which is where a sitar's halo of resonance comes from. There are a lot of them, they take time to tune, and the tuning depends on the frame you are working in. Replacing the whole set is a long job; replacing one is not.
Buying strings
Sitar strings are sold as sets by instrument style and pitch, and the gauges matter more than usual because the tension is what holds the bridge and the neck geometry in balance. Do not substitute a guitar string of similar diameter for the main string: the material and the way it takes a bend are not the same, and a bent guitar string will not behave the way the technique expects.
When to change them
The main string, whenever it starts sounding dull or refusing to hold a bend cleanly. The sympathetic strings, when they will no longer come to pitch or sound dead — which happens slowly, and shows up as the instrument seeming to lose its resonance rather than as one obvious fault.