These old wire "coathanger" style shift linkages are known for failing in this sort of manner - though usually is is at the front end and not the back end..
There are replacements available from BMW, and our forum moderator, Justin B, had been making some very robust and adjustable ones in his home machine shop and selling them to members here - I don't know if he has made any recently, but you could ask/private message him. I -and a number of others here - are very pleased with these units and it definitely makes shifting a much more positive experience.