There should be no premature termination issues once you properly set the target group (all html files in this case). And any time you change the search or replace term or any of the controls, a new search is auto started. That said, I will still try to reproduce it.
FWIW, all of what you describe would be better done with Filter Replacements, please give it a try. It should be much faster than your one by one approach with no errors as you can see the change in context before you decide it this is a problem case or not.
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