I suddenly am unable to connect to my 2nd Gen iPod Nano via iTunes.
Did they drop support for older iPods in iTunes 12.7?
No, iTunes 12.7 works just fine with older iPods.
I have just synchronized an iPod mini 1G (2004) with iTunes without any issues.
Try unplugging and plugging back in. iTunes will ask to download and install iPod support software. iPod Nano 2nd generation still works great with the current version of iTunes i.e. iTunes 12.8.