EDIT: thank you for opening the Issue. Thinking twice .. I know what is the problem, it is a side effect of a 2.0.9 improvement which happens only for new users of the add-on. And it happens only during initial favicon fetching. I will correct this overlook in 2.0.10. Sorry for the inconvenience.

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Hello syncup, strange, this normally only happens when there is a modification to a bookmark in background ... which should not be often at all ..
Would you mind opening an Issue here -> https://github.com/aaFn/Bookmark-search-plus-2/issues ?

A few questions, if you can add corresopnding answers in the Issue:
- do you have any other add-on related to bookmarks installed besides BSP2 ?
- is the refreshing persisting all time and until you close the search pane, or stopping after a few moments ?

Thank you, aAfn.