If your saddle comes out that readily, it's too loose. You should almost (!) be able to pick up your guitar by the saddle if there are no strings on it. Why? A snug fit ensures that the saddle doesn't lean, in effect shortening the string length and screwing up the intonation. It also ensures good coupling of the string to the soundboard over the saddle/bridge, improving tone and sustain.

My advice is to get a proper saddle cut, and yes even the finest guitars sometimes come with lousy saddles, particularly if there's been an aftermarket installation of a pickup. Do not shim! Lots of good saddle materials out there, but I prefer bone.

A simple pencilled 1 or 6 on the relevant end of the saddle below the top of the bridge will solve your problem in the meantime.

Peace, Mooh.