two questions to better undertand your situation:
Anyway, you should take the logs from the Forwarder using the TA_Linux (https://splunkbase.splunk.com/app/833/) but the detection of server down usually is done using the Splunk internal logs: if you have Splunk internal logs from that server the server is up otherwise is down.
You could say that in this way you can only know that the Splunk Forwarder is up or down but even if the server is up and the Forwarder is down you are blind, so the best thing is to check the status of the Forwarder.
So, have you the logs from that server in Splunk? you can check using a simple search:
if you have results the Forwarder is up and running, if you haven't, you have to debug why, but it's a different problem.
let me understand:
is this correct?
how do you have the status of down?
which app are you using for monitoring the server?