There's two way to deal with this: find players who appreciate your GMing qualities and turn up for your games; or change your style and run adventures that are loosely connected, if at all.
You may actually end up with two groups, like me.
In addition to the game I run at home, complete with plot lines, recurring characters, personal character goals and all that, I play/GM in one group where player attendance varies widely. This game is at a club house and on an average night, about half a dozen games in different game systems are being played.
The D&D group at that club has three core members, myself and two others, who take turnns GMing, plus five or six others who join occasionally, depending on what other games are on that night. Sometimes people bring guests. Most players have several characters going at different levels, so they'll be able to join even if the other PCs that night are all only second level and their favourite wizard/fire elementalist is 10th going for 11th level.
In these circumstances, there's not a chance in hell you can run any involved game, much less one with slowly unfolding plot lines and deep character development.
So what we do is run short adventures that will be completed within two or three sessions. (One GM uses Dungeon modules a lot.) If most of the PCs change in mid-adventure, fine. As long as one of the original group remains, we regard the adventure as intact. Naturally, things may get a little tougher if the group changes and shrinks as they approach The Big Showdown ... but that's life.
I will accomodate for varying player attendance to prevent an automatic TPK, but not much more.
I was pretty sceptical at first (and still prefer my home game - how couldn't I?), but actually I find that club game very relaxing - tons of fun, plus great for cutting back your ego as a GM. I'd almost forgotten that you don't need to be a world-class plot designer to run a perfectly enjoyable game.
Let us know what you decide on and how things work out!