If I understand correctly, your Aufenthaltserlaubnis falls outside of EU free movement law. This should mean that the status it confers does not depend on the outcome of the Brexit process.
In addition to that, you are currently entitled to a right of permanent residence under EU law, and that may change as a result of Brexit. But since this status is additional, it should not be critical to your ability to stay in Germany, but it might be critical for others reading this message.
The draft withdrawal agreement provides (in Article 15) that a right of permanent residence acquired before the end of the transition period shall endure after the end of the transition period. It is, however, a draft, so it could change. Such a change is unlikely. Things would have to become very bad before UK and EU politicians would disrupt the lives of tens or hundreds of thousands of people in such a manner.
As I was helpfully reminded by Janka, however, there's another possibility, which is a "no-deal Brexit." In that case, there are several possible outcomes:
- EU courts decide that your EU citizenship somehow survives Brexit. This seems implausible, but the theory is being tested in a case in the Netherlands. I was looking for more information about that when the europa.eu became unavailable. If your EU citizenship survives Brexit, your right to reside in Germany would as well.
- EU or German courts decide that under some other legal theory your right to reside in Germany survives Brexit. For example, forcing UK citizens to leave Germany might be found to constitute a violation of their human rights.
- Germany unilaterally modifies its law to allow UK citizens already in Germany to stay.
- You have to leave Germany
It seems to me that the last is the least likely. The next to last seems most likely, especially if neither of the first two possibilities comes to pass.