Are you sure this has anything to do with ARP? The 1920 is a layer2 switch and doesn't need to do any ARP.
I'd suspect it has more to do with the subnet size especially the DHCP scope. Once IP address allocation is exhausted - which for the most common /24 subnet size is 256 (or rather 254), you need to enlarge the network. If you've just got this single subnet it's not too hard to do.