I remain unsure. I accept the reasoning behind the answer above well enough ("mein" has to get its gender from somewhere), but why the distinction: "Without a noun..."? They use gender with a noun as well, correct? Maybe it was just confusing the issue? Or am I missing something?
Possessive determiners like mein/dein/ihr/unser/etc. follow the declension pattern for the indefinite article ein. That means that there are some combinations of case gender that require no ending - for example nominative masculine: Das ist mein Hund.
Possessive pronouns (technically they're only called this when they replace the noun completely, i.e. don't have the noun following them) however follow the declension pattern for the definite article der. That means they always need an ending, even in those situations where they wouldn't as a determiner: Der Hund ist meiner.
Think of these two categories as the difference between "my" and "mine" in English.