Often times what keeps an exclave loyal to its parent country is protection. Throughout history, exclaves have depended on the military forces of their parent countries. In many instances, the parent countries received some economic gain from the exclaves.
For example, the exclaves might have large amounts of precious metal, fuel or some other commodity. Thus there was an exchange of protection provided by the parent country for items of wealth from the exclave.
Exclaves don't usually seek independence as long as they fear military actions from the countries surrounding them, regardless of how much they may dislike the parent country.