Shelf life of a yogurt product
Mast O Khiar, as you mention mainly consist of plain yogurt and cucumbers and most recipe do not require much more than that. Because of such, the shelf life for the yogurt product will be the shelf life of the yogurt itself. If it is a store bought yogurt, then the shelf life should be about 2 weeks in the refrigerator.

Make sure to store the sauce in an air-tight container. Most tubberware should work. Those soup containers from Chinese takeout orders work perfectly.

EDIT: After a bit of a debate in cooking chat, I decided to change my answer a little. The reason I said 2 week is because personally I had eaten 2 week old Mast O Khiar. However it could be recipe dependant so it could be different for a different recipe. 

However it is very easy to tell whether yogurt OR cucumber is bad.

Mast O Khiar should have a very fresh/clean aroma. When yogurt turn bad, it releases a rancid smell. If it smells bad, dont eat it.

If you see fuzzy mold it's a good idea to throw it out.