Keblerelf is right, but i can give you a more technical version: there is a bug or some sort in the buffering system of brawl. Even though several moves can be buffered slightly before we actually do them (and we buffer moves all the time, without noticing) the grab button's buffering is messed up. The grab button input is a simulation of Sheild+attack input. Because of some issue with the buffering, the attack bit gets dropped, and if you buffer a grab, you get shield instead.
L+A, i think works better. However, if you tap the grab button when you are actually able to do stuff, you'll do a grab fine. (you can also accidentally shield if you hold the button down too long i think.)