It's been a week for my WordPress being unable to resolve some external host services via URL address. It was working for a while, couple of months, with no changes by my side, and suddenly the dashboard RSS and stats data stopped responding. The error was: 

RSS Error: WP HTTP Error: Couldn't resolve host 'blogsearch.google.com'

I haven't changed the httpd.conf file recently, neither the PHP settings or something. I thought about any possible update settings from my Fedora system, but no clue.

Restarted the apache server few times. The /etc/resolv.conf file was standard. One of the common failures is DNS server change and no flushing/refresh from the Apache. But mine was still there, no changes applied.

The solution was calling the httpd process via strace. It's been auto magic - just call it once via strace, then stop or kill the stracing process and start the server as normally. It worked here.

So, I stopped my apache server (which is in /usr/sbin/httpd here, could be in /usr/local/apache2 or /opt/lampp or somewhere else) and I reincarnated it that way:

strace -f -s 128 -o dbg /usr/sbin/httpd -k start

Once debugging started, the services updated by themselves. I killed the service and ran it again as usual:

/usr/sbin/httpd -k start

and everything went back to normal.

Thanks to maniax for the help