E-brake cable on 90 LeSabre

My emergency brake cable does not always work. It seems to be properly adjusted underneath the car, but now seems to have a new problem. Underneath the dashboard there is a lever that connects to the emergency brake cable. The problem is that after engaging and releasing the e-brake, the cable does not stay attached to the lever. It seems to "pop" out of place leaving me with no e-brake. Does anyone have any suggestions on how to properly fix this?
Thanks!
Leo
90 LeSabre Limited

Also, thanks to everyone who helped me with my reverse lights a while back. I was able to adjust the switch on the transmission and now they work fine!

Recheck the cables under the car. Pay special attention to the two cables that go to the rear wheels. One of these cables could be rusted up or binding and frozen.