I get this same issue on my Galaxy S5. Wifi is on, and active. I've tried setting the update to happen one minute in the future and gone out of the app, and continued to use the phone/wifi through other apps to make sure wifi isn't sleeping or something like that. This does not eliminate the problem.
I've tried logging out and back into the app. I've also tried the latest response of entering *#0011#. This does nothing (pressing call after typing that sends me to an automated Verizon line that says my update feature is invalid).
I can get the scheduled backups to work if I enable the setting to allow use of Cellular data (instead of just wifi). This is obviously not a desirable workaround.