The asterisk log file (/var/log/asterisk/full) shows entries like this:
[Sep 3 04:02:08] ERROR chan_sip.c: Serious Network Trouble; __sip_xmit returns error for pkt data
Solution: The server had been moved from one public IP-address to another. In Asterisk PBX settings, the fields for both External IP and Bind Address (under Advanced) needed adjustment to the new IP-address. After server reload everything worked normally.