The IP address should NOT be changing when you “unmount” and or "mount a “drive”. Where the IP address “might” change is when either the router or the My Cloud is power cycled.
Not sure why you don’t want to use a Static IP as it tends to solve the problem of the IP address being reassigned. One can set the static IP either in the router OR in the My Cloud, or as the previous poster indicates change the DHCP server’s “lease timeout” period to infinite or never expire.
If one isn’t using a Static IP then the DNS should be being pulled from the router when it hands out the IP Address to the My Cloud. Like the previouis poster indicated power off both the router and the My Cloud. Wait a few minutes, then power on the router and wait for the router to finish booting up and enter an online state. Then power on the My Cloud and wait till the front LED turns solid blue. Then attempt to access the My Cloud Dashboard.