OMV disappears from the local network when it is not connected to the Internet

I have a strange problem with the OMV machine. Raspberry Pi 4 2GB RAM connected to the local network with a network cable, OMV 6. Currently I have a directory shared on it via SMB. Everything works fine, GUI in the browser, network directory, access to raspberry pi via SSH. I connect to everything by IP address. Everything changes when I disconnect my local network from the Internet. Every time my ISP fails or I disconnect the internal network from the external one, OMV disappears from the local network. The IP address does not even reply to a ping. Everything returns to normal when Internet access returns. I've been thinking about it for a long time and I can't figure out why. I have a few other raspberry devices in the local network, but the problem is only with the machine with OMV.

It connects to OMV by IP address so DNS should have nothing to do with it but I found suggestions like this on a few forums so I checked a few things. As part of the test, I changed the DNS address for OMV to a non-existent address. With the Internet working, the device was still available in the local network. I switched the computer from which I connect to OMV to the non-existent DNS. Of course, I lost connection with websites on the Internet, but OMV was still available, which rather confirms the fact that when connecting to OMV via ip DNS, it does not matter.

Does anyone have any suggestions?

Thank you for your answer. Unfortunately, that was not the case. I have a static ip set up on a machine with OMV. The problem is with my local network, and more precisely with the router. It turns out that the Tp-link equipment from the Deco series has a certain ailment (known for years) that the manufacturer does not intend to fix or cannot do with the software update.

The Deco router (M4 in my case) has 2 ports, gigabit. The first is that I am plugged into an ISP's WAN. I have the second port connected to a gigabit switch that creates my wired LAN network. It turns out that when the Deco device loses communication on port one, it also stops communicating on port two. As a result, all devices connected to the network via a cable are no longer visible. Only WiFi works. I found the first mentions of this problem on forums with the date 2019. To date, the problem has not been solved in the latest deco firmware. The manufacturer distances himself from the problem. Everything indicates that I will have to replace the router.

Either way, neither the OMV nor the raspberry pi are affected. I should have checked my network more closely before I posted the original post for which I apologize.