Gemini and Sagittarius have a lot in common. They are opposites in the zodiac, which would sound as if they don't have things in common. But they are the most perfect, in a sense, opposites, because they share a love of life, a love for adventure, curiosity, a wide circle of friends. They enjoy getting out in life. Each of them is very independent, and each of them does like the sense that life is and adventure. So as opposites, they work well on that level.
What's opposite about them, however, is that Sagittarius needs a great deal of freedom. Of course, so does Gemini, but Gemini is willing to be in a relationship and really look for a soul mate, look for a twin soul. Gemini is the sign of the twins, and so on a psychic level Gemini looks for another that will be just like him or her.
Sagittarius doesn't fit that role. Sagittarius is someone who really wants to explore life on its own. I don't mean without a partner, but basically does not like being in tandem. So one is looking for a partnership, and one is looking for a solo adventure. Over the long term, as alike as they may be to start with, they drift apart because of those issues between them.