Does saying ''I don't know" often decrease my authority as teaching assistant?
Is it a true phenomenon that the respect on TA decreases with an increased frequency of I don't know replies?


Certainly not in the sense of "you have 5 'I don't know' per semester, and then you lose the student's respect. It really depends on what questions you do answer, how you answer them, and what kind of questions you are unable to answer.



If you normally provide good, instructive answers to questions with the occasional "I don't know" mixed in, no reasonable person will lose respect for you - especially if you commit to finding the answer to the questions you are unable to answer, and then follow through.

That said, it depends on what the questions you aren't able to answer are. If those are questions that could in a very similar scope also be on the exam, not knowing the answer (and not being able to derive it in reasonable time) will indeed not reflect well on you. If that is the case, preparing better for teaching the course (or teaching courses closer to your field of research) is really the only way forward. Otherwise, the students have all rights to be annoyed - what could they learn from a teacher who doesn't sufficiently master the course themselves?


  I worked as a TA for several courses. Some courses fall into the domain in which my research also happens. But some other courses are not at all familiar to me.


Maybe I'm stating the obvious, but that's really not the student's problem. The students should have an expectation that their teacher is qualified to teach the course, whether it's in their area of research or not. You should not expect leniency from the students because you are teaching a course outside of your field of research.