Nougat doesn't include its own firewall (well technically it does -- iptables is integrated in the kernel, but it's not enabled) so it does sound like it's just a matter where the upgrade altered some networking aspect that messed up some setting in your SSHDroid configuration. Try going into your app manager, tap 'Force stop' and then 'Clear data'. Then start up SSHDroid and since you did 'Clear data' the app is basically starting from scratch, so you'll need to reconfigure it the same way you did when you originally installed it.
Also, maybe give some thought to also upgrading to a different SSH app, SSHDdroid hasn't been updated in almost a couple of years (Aug 2015). Currently I use JuiceSSH but have read glowing reviews about ConnectBot.
ConnectBot
https://forums.androidcentral.com/e?...token=U9hLFw8Q
JuiceSSH
https://forums.androidcentral.com/e?...token=3BWOKE-Z