I drive an 03 SE maxima.
My fuel gage reads full when I fill up but stays there until I am almost out of gas, then it drops to right above E.
What's the problem?

 

Your fuel pump sending unit flow probably stuck or rusted due to condensation in the fuel tank. I would pull it out when you are on empty tank so you can see if the contact on the sending unit is corroded or the float arm is deformed