Either your problem is not related to Admin Tools, or you are not telling me something important.
Try to set up a Super User in the backend of the site. When you get blocked go to Components, Admin Tools for Joomla!, Web Application Firewall, Blocked Requests Log. You should see your IP address there. What is the Target URL and the Reason you see?
If you do not see your IP address at all: it's not an Admin Tools issue. I have seen a lot of servers which do block URLs in Joomla's backend because of unfortunate server protection rules. Your host can check that, and tell you what to add to your .htaccess file to disable this rule on your site.
Nicholas K. Dionysopoulos
Lead Developer and Director
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