I currently have a render farm where all the machines are connected and are working fine. One of the machines can’t connect to the internet and as a result it means all the other machines can’t connect to the repository for some reason. The other machines are connected to the internet via ethernet fine.
I don’t think it’s related with fact one of your machine isn’t connected to the internet. Our whole farm is disconnected from internet and works just fine. What is your Deadline server OS? Isn’t there limit of concurrent connections?
So we have 5 machines in total, three of these machines are on windows 11 and two are on Windows 10 if that’s what you’re asking regarding Deadline server OS?
The repository is on a shared network drive too.
Could you please elaborate on what you mean by concurrent connections please? 
win 10 and 11 Home version has limit of 20 concurrent connections. For you is it ok as you have 5 machines in total. For bigger amount you need have server version of OS which allows much higher number of simultaneously connected machines.