Drupal - The server can't issue HTTP requests

I don't regularly check the status of my Drupal server so only after several weeks I realized that Status Report says The server can't issue HTTP requests. It was clear that Status update module doesn't work correctly. When I tried to fix this problem, I have to fight several unrelated problems:

Due to unclear reasons, probably bug during downloading module status from Drupal site, provoked a call to function system_check_http_request()Drupal site works by sending request to admin/reports/request-test. Unfortunately my web hosting has disabled downloading data from URL's on the same domain (they say it is pointless...), so an error was detected and drupal_http_request_fails variable was set to TRUE. From that time on Drupal was thinking that my web server doesn't allow to issues HTTP requests to any site.

In my first attempt to reset this variable I used MyPHPAdmin, but it did not helped, Drupal caches the value.

The second attempt to clear the variable using Drupal module http_request_fail_reset was also unsuccessful because after I activated the module, Drupal went crazy (No response from server). I later realized, that when new module is activated, Drupal immediately tries to get module Status, so it calls the defuncts Update status - Catch XXII.

The last attempt to clear the variable was with usage of module Devel, now I was successful. I had to disable Status update module, see previous paragraph. I had troubles with Devel module, because it doesn't work well with I18n module and menu items are not shown in menu. And more - the Devel module cannot change drupal_http_request_fails variable - Sorry, complex variable types may not be edited yet (boolean is too complex??), so after all I used MyPHPAdmin and Devel to clear caches.

I enabled Status update module and everything seems to work correctly.

Some notes:
Variables are in table variables.
Modules are in table system, column status is boolean, 1 = modul is active, 0 = modul is disabled.
Menu items of Devel module can be found in function devel_menu(), file devel.module.