Just a SWAG: how about rewriting all current direct JS calls to statcounter from your pages into function/Ajax call into your own server ? Dunno the effort, but you could try to bribe an officially retired coder to munge all such pages with some code in a language with nice string functions.

Less reason to block such Ajax from clients, easy for you to forward the call to statcounter with data scraped from clients from your server keeping analytic scripts in place.

Of course piping the data into table(s) on your server as backup solution easy to do -
if statcounter has problems data is already saved/safe...

>For some fifteen years I was using statcounter.com as the visit counter on my website, and it worked swimmingly. Until about 2016, that is. Then the number of recorded visits started to fall, and the annual graph became a bell curve. Now the number of visits per day dwindled o a couple of dozen, and monthly fell below a thousand. For a few months I had my autobiography published there, as an experiment, and I've noticed, from feedback from friends who emailed me some comments, that their visits weren't registering at all. And it's not geographical, e.g. there was a guy from NYC and another one from around here.
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>So I went into the admin pages of my site and found they have added some Webalizer thing, which seems to be a third party app serving up the statistics from their hosting server's logs. And guess what, it turns that the traffic wasn't dwindling at all, it's just that the statcounter script wasn't executing for an increasingly larger number of visitors. So, for current month, statcounter reports I had 414 visits so far, while the webalizer counted 20293 on http plus 43311 on https.
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>The way it worked was that there's a script in each pages, which would set a few js variables, package them into a http call, and submit that to their server, which would then write a record somewhere. Now I'm thinking that, what with the overall web paranoia, this gradually got more and more filtered out, and that the call to their server simply got nowhere.
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>Now I'd hate to drop the automation I built around statcounter - I wrote a little script which called their API and got the current results every fifteen minutes (more or less, somewhat randomized), so I'd get the data regularly. But then if the data are (ARE! not is!) unusable, I'm ready to cut the ropes and let the sandbags fall.
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>Does anyone know more about statcounter's current status?