Without any further information on the application, e. g. is it web server-based, native, etc., it is hard to tell.
From the operating system perspective, one possibility is using tcpdump and filtering on that specific port. You could generate your own log files that way and process them as needed.
Another solution would be to use iptables, but this will most certainly slow down your system performance.
From the network perspective, you could use netflow (if your network devices support this) and grab the connection data.
But all of the possibilities listed are NOT retrospective. For the PAST time, there would not be a chance.
Maybe your network guys can help? They might have connection or traffic logs on their devices.