You cannot reconnect, but everything that is printed with -printtoconsole will also be written to the debug.log file. So you can just do tail -f debug.log to get the same output.
If you wanted to monitor for errors in this way, I would suggest that you always do tail -f debug.log instead of using -printtoconsole. The debug.log will always be written to so you can look at previous logs while you are offline/away. And it is still written to when Bitcoin Core is daemonized (with -daemon) or otherwise running disconnected from your shell (as in your case).
