These symptoms can have other causes but they are commonly caused by a poor
antenna connection, either at the radio itself or at the antenna.

Don Young

FYI, a loose antenna connection may be causing this and there is one
particular spot where the antenna wire can come loose on this year Malibu.
If you remove the plastic kick panel on the passenger side and pull the
carpet back a bit, you will see the connection I am talking about.  This
happens after a few years of passengers pushing on the connection with their
feet.

The most common symtom of this connector coming loose, however, is bad FM
radio reception, not AM.  Still, it is worth checking it out.  Good luck.

Sharky