[support] Failed to fetch available update data

Hi, my site is using drupal 6.22 and for two or three days I'm having this strange problem:

Whenever I try to check for available updates for modules/core (/admin/reports/updates/check), either I get no data at all or I get info only for a few random modules (and that after exceptionally long time of waiting, a few minutes). Right now only for three out of twenty. For the rest, only message "Failed to fetch available update data".

Where is the problem? Everything worked as expected till about the middle of the last week. Of course I have not changed anything on my site. And it does not help to "check manually", it is still the same: for a few modules I get info, for most of them nothing...

Jarry