This is my intermediate knowledge getting in the way, but why can't the MAC address be used to reconnect to the DNS Server? This causes the usual issue of losing the IP's so I have to run around and re-setup statics IP's. The Network printers and handhelds will grab a different IP. Like I said, just a guess, but it would certainly explain whats going on, especially if it's always the same devices that this happens to. Thankfully, it happened on a Sunday, so I only had a half dozen users impacted. To make matters worse, I had not DOCUMENTED the configuration. Other power outages had occurred, but they were short enough that the battery backups kept the switch from ever loosing power, so I had no idea I had forgotten to save the configuration. It had been that way probably a year or more. Came down to a managed switch where I had setup some VLANs to route traffic, but never SAVED the configuration. I had a major network outage after a long power outage a couple of years ago. I'm not aware of particular brands of printers that might behave this way, but a LOT of network routers/switches/etc (Cisco and HP/Aruba come to mind) will do exactly this.
Without taking the extra step to save the configuration, the device happily plays along on the static IP you have set, but upon a power cycle, since you didn't save the configuration, it reverts to whatever configuration it had the last time settings were saved. Not knowing the brand of the devices having these issues, I will venture a GUESS: After setting the static IP, there may be a SEPARATE place where you need to go to SAVE the configuration.