I don't think dnsmasq error is relevant right now.
@enrico.s you need to do one test and time and check the result on your machine:
1) Connect with the monitor, try to login, and see what happens
2) Check the network connectivity, try some ping and ssh to other machine from the server iteslf
3) You absolutely need to find the moment when the server stops working and see the relevant logs at that time
Everything sounds to me like a network problem, I'd bet on a conflicting IP