Answer: In my experience jasmine really prefers a humid atmosphere and so it is possible the buds are simply in drier air than they would like. This is especially possible if it is in a cool dry draft from an air conditioner. You might try setting it in a pebble tray to try to increase the humidity around it. You also need to be sure that your watering is effective. The water needs to penetrate the root ball so that it is moistened thoroughly, so you might check and be sure it is not running out between the rootball and the sides of the pot. Finally, check very carefully for signs of insect activity both outside and inside a bud or two.
There are a number of types of jasmine and based on your description it is unfortunately impossible to tell which one you have. You might try consulting the websites or catalogs of some of the tropical plant specialists such as Logees http://logees.com/www/ and Glasshouse Works http://www.glasshouseworks.com/ to see if you can figure out which one you have.
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