Would drinking diet coke too much for a long period of time permanantly damage your teeth?

Yes: The phosphoric and carbonic acids in diet soda when left sitting on and between your teeth erodes the enamel significantly. Your teeth may become hyper sensitive and yellow as you dissolve the white enamel off of the yellow dentin beneath it.

Absolutely: Many diet drinks, coke included, contain high levels of acid. Usually phosphoric and / or citric. We use phosphoric acid to etch teeth when we fill them so the bonding sticks best. What is happening is you are creating little (or big) pits in your teeth as the acid eats away at it. Sipping all day is the worst. Chase your drink with water, or quit it entirely.