I suspect an issue with either the head unit itself and/or the wiring for the stereo. I have had a couple of e28s myself and have used far more modern headunits (mostly Kenwoods as I am a huge fan) than the CD43 and never had issues using stock e28 cabling or speakers.

I have also upgraded the stock stuff as well including speaker wires as IIRC they are only rated for 10 or 15 watts

Try the CD43 in another 80s or 90s era car - If you have that option. If you still have the problem its the headunit. Also tyr a different head unit in the e28 and see what happens