There could only be two reason of AP changing IP, 1) The DHCP lease time is set to a week or 2) The AP reboots and since this specific IP is not reserved on DHCP for this specific device (and neither set to static on AP) it receives new. Coming to your question Yes you should assign static IP for the AP.
Actually this is a bit weird. Mostly all DHCP servers tend to reassign same IP to the device, when lease is renewed. If AP receives a different address, it may mean that there is a gap, when AP isn't available, and specific IP is issued to different device.
Anyway, actual IP address of AP is irrelevant for clients, as they never communicate with AP on L3 - for clients AP is just a L2 hub connecting them to the backbone. So it seems that you have more problems than just changing IP address.