Release a socket back depending on whether they are live or dead in its own pool?

Say you are at home, you have cable plugged to your laptop, and router, and behind router there is cable modem. If you turn off your router - your laptop will know that - no voltage. If you turn off your modem... that goes tricky. You simply can't know that. One potential problem is no route to host. But even if you are connected, it can be any other issue. Some protocols - like ssh have ping build in - so they have keep-alive for connection. If your app is doing nothing every interval there is ping-pong between client and server, so you know if that is alive.

If you have full control on the protocol - keep-alive is one of the options.

Your client is at one end, but in general it is really hard to have two parties be sure that they have agreement. Byzantine generals problem describes something that is general network model, where each node is not aware about any other, and can trust only what is aware of.

In general I would not write distributed system myself. I'm using Hystrix for that. Link is to their configuration, so you can see how big it is. You can track if the server is working, or not. Also when it is back again you can prepare policy to figure it out, not to flood it, cancel messages that are outdated, and many more - graphs, stats, integration with other solutions. There is big community using it, and solving problems. That is much better option then doing it yourself.

Not sure if you have only this one service to talk with, or if Hystrix is for you good way. In Java people tend to use layers, frameworks if they deals with problems... Hope it help.