1996 740IL RADIO SHUTS OFF AND COME BACK AFTER A WHILE, WHAT IS THE PROBLEM

Corrosion at the fuses. One in the fuse panel, one on the back of the radio. Could be a bad solder joint or component in the radio.

Peggy, Is the radio actually switching off or do you just loose the radio station. If radio is shutting off, there must be a bad wire/ plug connection, loose plug, or maybe bad ground.
If loosing station, have Arial/antenna connections checked, maybe upgrade to better antenna. Some stations just do not send out a strong signal which can also cause loss of station.

is it an after market radio? if so it might not have enough power so it goes to pull power when its turned up and its not there so it just shuts off. try checking your radio wires and your fuse.

is it an aftermarket radio? it sounds like the power wire is tapped into the illumination wire.

Check or replace/repair the K134 multi function relay module located under and up the dash on drivers side. Its about the size of a pack of cigarettes and gray in color.

I opened mine and re-soldered all the components on the board. I had radio going on and off, trunk not opening, sunroof with mind of it's own, and dying battery.

All was solved with this module...under $100 at the dealer if you don't want to goof with it.

Bad ignition switch or an adjustment. Your talking,electrical switch here, not the key cylinder.

Sounds like a fault in the connections at the back of the radio, possibly earth, you will need to remove the unit and check.

Sounds like you just have a bad connection at radio power wire. Check radio fuse first to make sure it's o.k. but then you'll have to get someone to trace power wire to back of radio & check connections.

Likely bad ground. Also check battery voltage when headlights are on. Most stereos shuts off when battery level drops bellow certain value

Radio has an internal problem.