I did a rewrite of the receiving part of my driver. Now there are no unused RX Descriptors anymore. Furthermore all rx processing is now inside a task, a receive interrupt just gives a semaphore to start processing (the take-semaphore action times out every 5 ms to check for a BD marked as non-empty even if there was no IRQ).
Still the problem persists, that after a while the reception of Ethernet frames stops. The receiver is still enabled and all (4) RX BDs are set to "empty".
The question is now: What (suddenly) keeps the MAC from proper reception?
I am now going back to the previous version of the MAC, since this seemed to not show this behaviour.