I am not very familiar with home automation systems, but I looked up the Z Wave system and see that it uses the 900 MHz band. The not turning on and off issue could be caused by interference from other devices. I would find out what frequency bands all of your wireless devices are on. I would also obtain a 900 MHz spectrum analyzer (
www.rfexplorer.com), you would need one that works for the ISM band - 902-928MHz and 2300-2500MHz. Some utility smart meters operate in the 902 -928 MHz band and form a mesh network throughout the neighborhood. How you would do the test is check for activity with the spectrum analyzer with all your devices on and then with all your devices disconnected (meaning all the Z wave controllers powered off). If there is lots of activity on the 900MHz band with all your devices off, there may not be a lot that can be done. This is a complex subject, but the 902-928 MHz, 2.4GHz, 5GHz, and other frequency bands used for wireless devices are a limited resource and have only so much space for devices to operate. If there are smart meters nearby using the same RF space as your devices, the neighbors have similar systems, etc. there will be problems. This is only going to get worse as more people use such systems.
I am NOT against smart meters, but it was a poor choice for manufacturers to put them on the unlicensed ISM bands along with consumer devices.
Another issue with these systems is that if they are using apps on your phone and an account that you had to set up with the manufacturer, there is always a risk of hacking by unauthorized persons, security of these systems are partially in control of third party servers and the manufacturer.