Really depends on sooo many things:
What kind of cartos are they? Some brands/types last longer than others. I've had really good luck with horizontal bottom-coil ones.
What are your liquids like? Certain flavors/mixes are harder on cartos than others. What happens is that they gunk up the coil with diamond-hard carbon crud that's nearly impossible to remove. Once the coil gets cruddy, the liquid can't get to it to heat up and produce vapor. Chocolate/coffee/sweetened/dark flavors tend to be hard on cartos, as does higher VG content (I like 80PG/20VG).
How do you clean them? Some cleaning methods are more effective than others. They're all pretty effective at cleaning the poly-fill; the problem is getting the stubborn crud off the coil.
...and it goes on and on...but even with the worst conditions, I'm guessing you should be able to get maybe a couple of cleaning cycles out of them.
I've been fiddling with regular cartos for over a year now (waaay too long) and am just waiting around for the next fillerless carto to come out to get far away from them. Regular cartos are a PITA to clean. The CE3 comes close, but there's still a love/hate thing with those that I'm not willing to go through. The Stardust/Vision/
tank type stuff isn't too bad, but they're either made out of the wrong plastic or look goofy on my stick batts (which I still love)...so still waiting...