I am having the same problem. Have not been able to update for five days. I filled out an online help request form. My internet is definitely present and everything works fine with the exception of AdGuard which cannot update itself. :-(
To be clear, the filters will also not update. As a result of this, there is a conflict with Amazon Prime Video which locks up the page. I can run a tracert to the update server with no problems, and AdGuard allows me to refresh the license information without problems. It just cannot auto-update the program or the filters. It all comes back with an error.
UPDATE 02 JUNE 2019:
Since tech support does not appear to be forthcoming, I'll continue my reports. This morning I completely uninstalled v7.0.2693.6661, then deep cleaned the registry to get rid of anything that might be hiding, and re-booted. I then re-installed the same version and guess what?!!! Absolutely the same damn problem! The problem is not on my end. It is with AdGuard's server or with their Cloudfare settings. C'mon guys, fix this!!! I have not been able to update.