Reading a paper on Descartes I found the following summary of criticism:
Stuart Hampshire, on the one hand, emphasizing the indubitability required of the principle by Descartes, concludes that its denial must be supposed to be self-contradictory in order for the principle itself to be logically necessary. "But philosophers since Kant are generally agreed that no proposition that asserts existence in this way can be logically necessary." On the other hand, D. J. O'Connor argues that if the principle is logically necessary, then, "Descartes' famous cogito, ergo sum is merely an analytic triviality. For the word 'I', like all personal and proper names, is an index sign which cannot be meaningfully used except to refer to an existent particular." Descartes seems caught on the horns of the familiar analytic-synthetic dilemma: no statement can both assert existence and be logically necessary. There are no synthetic a priori statements concerning existence.
I'm not surprised by that statement, I'm just wondering if that's really an established dilemma, as it's depicted here, and if somebody knows of any papers addressing it in more detail, so I can do some reading on that.
Also, if you happen to know by heart where in the Critique of Pure Reason Kant addresses that topic (I suppose it has something to do with his rejection of the ontological proof of god, but I don't remember where I read that), please let me know.