In a much earlier discussion (see here) on the Twonky time out issue some modified the ssdp_beat_time to 3620 from the default value of 1810. Remember to restart the Twonky server (or just reboot the My Cloud device) after making such a change.
Other troubleshooting suggestions. Configure the My Cloud for a static IP or better reserve an IP address for the My Cloud in the router’s DHCP server administration settings. If the device streaming from the Twonky media server/My Cloud is connected using WiFi, monitor the WiFi on the device and the router to see if the WiFi signal is the cause due to dropouts or relogins. Test if other devices exhibit the same issue when streaming from the My Cloud.
