ReadyNAS 2120 disconnects from network

While it would be unusual for it to occur in 4 years, it sounds a lot like a power supply issue.  The NICs and the power on/off circuit have an independant power called +5VSB (+5 Volts Standby) that stays on all the time, even when the NAS is "off" via anything other than the rear switch.  Holding the button down to power-off should be independent of any software, so that not working points to hardware.  The NIC uses this power so WoL works, BTW.

The warranty on a 2120 is, I believe, 5 years, so you should start with that as your first option.  I'm sure they'll have some things you need to do to insure it's a hardware problem, not software.

If you are not the original owner, or not able to get warranty service for some other reason, then it's time to see if the power supply really is the issue.  Unfortunately, I can only find one picture of the insides of a 2120.  The case appears to be made by Chenbro (it uses Chenbro style caddies and has other similarities, as do the other current rack-mount ReadyNAS).  Their usual 1U power supply is a standard Flex ATX, but that's not what's in the 2120.  It doesn't appear to be anything standard.  It almost looks like it's just a single-voltage supply, in which case the +5VSB would be created on the main board, so a power supply replacement wouldn't even fix it.  The picture just doesn't show it well enough.