Is there a limit to EMDR? I think there certainly can be, but it's unique to each individual. I figuratively hit the wall with EMDR after a while. My first therapist and I realized it wasn't really helping anymore, so we just used it when I felt like it would help. She was very flexible and employed a more open version of EMDR which helped me greatly sometimes. When we moved to another state, I went to an EMDR specialist for a while. She was more rigid and less intuitive than my first therapist - very structured and focused on the protocol. After a bit, I felt like I was failing to progress and getting nowhere and just frustrating her with my lack of being able to properly work through the appropriate phases and come up with a target memory, negative belief, etc.
At that point, I actually called my first therapist (in another state by this point, and a year later) and chatted with her about whether you can really just reach a point where the usefulness of the modality is exhausted. I did stop seeing the EMDR specialist, and found someone else who uses EFT quite a bit. That one has been fairly successful in places where EMDR kind of failed.
Personally, I would say look for either progress or a lack thereof. It doesn't matter how great a modality "should" be if you aren't moving forward with it. I wish you the best as continue your journey.