There are at least two reasons for this.
First, General Henry Clinton handled the Southern strategy badly. He antagonized many in the South who might have been loyal to the Crown. He did this, for example, by promising freedom to all slaves who would come to British-controlled territory. This scared slaveowners and made more of them support the rebellion.
Second, the strategy used by American General Nathanael Greene was very effective. He practiced a strategy of making the British chase him all over while refusing any large pitched battles. This forced the British to try to "live off the land," which meant that they had to take supplies from local people. This helped to make the Southern populace oppose the British.
For these reasons, fewer Southerners remained loyal to the Crown and the Southern strategy failed.