Oh, hell! I take it back. It has nothing to do with grammar -- it's phonemic. From the Am Her dict:

thine (Zhn) pron. used with a sing. or pl. verb 1. Used to indicate the one or ones belonging to thee. adj. A possessive form of thou 1 1. Used instead of thy before an initial vowel or h: "The presidential candidates are practicing the first rule of warfare: know thine enemy" Eleanor Clift [ Middle English from Old English thhn; See tu- in Indo-European Roots.]