Apart from the obvious, the danger of the creation of a 'Greater Serbia' and subsequent loss of Austro-Hungarian territory, were there any other reasons? Perhaps the fact that other ethnic groups in the empire would also start demanding independence?
Giving in to the Serbians (which is what it would have been, since the Serbians didn't actually have any legitimate claims to the areas in question), would have set a bad precedent for the Tyrolean areas populated by Italy and perhaps most particularly the areas of Hungary populated by Romanians.
Italy was in the grips of a strong revanchism movement to recover the lost Roman glory, and they were the more organized political entity threat to Austria-Hungary. However, there was a much larger population of Romanians to consider, and the Hungarian administration of the region was much more oppressive than the Austrian administration of ethnic Italian areas. A movement to separate from Austria-Hungary and join Romania would have reached a more fertile ground than an effort targeted at the Italian population.