To properly diagnose, more information would be needed, I would get the codes that are produced checked by a proper diagnostics tool. Every system, including the electrical system, is checked and records what happens to it and those recordings will show on a proper diagnostics (what lost power).
I don't have audio at the moment so I couldn't tell, but does it primarily affect just the instrument cluster? Does it affect the audio system too? Those two are on the same control module system. Does it seem like it wants to kill the engine as well?
I have a 2008 335i and after about 50k miles I started getting random power loss that would mysteriously come back later. Sometimes it would even happen when driving, there hasn't been a recall issued yet (for some reason) but they traced the problem to the spade connector that connects the battery to the back of the fuse box which then feeds power to all the other electrical systems. I actually had a connector custom machined so that there wouldn't be the possibility of breaking connection again after replacing the fusebox and connector twice.
That would be a total power loss, no lights, no power to the motor, etc. It could be the battery cables, but we replaced the battery too, even though it checked out fine, and inspected the cables and they all checked out fine but you may want to have the resistance in yours checked as well to see there is a fault in the cable itself which is incredibly rare. The connector at the back of the fusebox is usually the culprit
If yours is not a total power loss, it could just be a faulty or loose control module, but I would get the codes checked.