Thanks for reaching out. I was testing this with our latest 7.3 stable nightly release. I had annotations in the document, I filtered by annotation state, and added new reply and comment and filter stayed same. In addition to that I followed my previous steps and added search filter, and still those filters were correctly kept.
If you are not using latest 7.3 version of WebViewer, could you try with that. We've done bunch of bug fixes to notes panel after 7.2 release.
Senior Software Developer
PDFTron Systems, Inc.