As far as "Being able to fly" for your whole career, the way I understand it is there is no limit (age or otherwise) as long as you can pass the flight physical.
HOWEVER, like Clux4 said, those "other duties" will be required in order for you to move up the rank structure and career. Those duties will keep you from the cockpit for a time. (Duties like OCS, TBS, Recruit Training, OSO, a "Staff" tour in Washington just to name a few.) Then you have those "mandatory" schools you have to attend in order for you to advance in the ranks (like Amphibious Warfare School).
Yes, you can definitely fly past Major, as a squadron CO, air group CO or Air Wing CG (though I don't know how much flying the latter two does. I'm pretty sure you have to be cleared for flight in order to lead those flying units).
There is also talk that a Marine Aviator will also command a Navy Carrier Air Wing (CVW) in the future. That aviator will/would be a full bird colonel. It makes sense because Marine F/A-18 squadrons have been deploying regularly w/ Navy CVWs for the last ten years now (that's nothing new, BUT before 1994, Marine Fighter Squadrons deployed with a CVW which seemed like once in a blue moon. With the disestablishment of a couple of F-14 squadrons, several CVWs only had one fighter element. So the Navy turned to F/A-18s to fill the void left by the disestablished F-14 squadron. Several Marine F/A-18 squadrons filled those voids). To be a CAG (a Navy acronym held over from WWII, to denote the Commander of a Carrier Air Group, before it was changed to Carrier Air Wing), you definitely have to be cleared for flight.
But like I said, a Marine Colonel as CAG is only in the talks as of now.
But anyways, to recap, as an aviator, there will be mandatory duties and schools that will keep you from the cockpit and there are times when you can still fly after Major. Remember you're a Marine first and aviator second.
