Port Time outs on Remote Hosts

I monitor all my servers using Nagios. Now, for Nagios to run certain checks, it has to connect to remote hosts via a certain port. Lets say the port is 8090.

Now, when Nagios connects to a remote host (for an example) via port 8090, and it has to run 6 checks (scripts) on that remote host, i find that it times out. Because, those 6 checks, depending on how quickly they finish up, can consume the port.

my question is, how can i make it so that a port can accept the maximum number of connections and can uphold those connections until the scripts finish?

i mean, say i have 15 requests/connections that are being sent from one central location to port 8090 on a remote host, what setting is it that determines how many connections/request port 8090 on that remote host can handle before it starts dropping them?

The application, I believe, it's part of its socket options when it does listen() and such.

Please post full details of the software which is listening on port 8090 on the target servers.