How to fix very slow server performance on OS X Lion?
If it is not responding to pings (meaning ping is returning "Request timeout"), then the problem is definitely not DNS or anything at the application level.  I see two possibilities:


Hardware failure: either a switch or network interface is failing.  Since you have another machine working (presumably) on the same switch, perhaps your ethernet port or ethernet cable have problems.  Try a different cable.  Try setting up another interface (perhaps via WiFi, or better yet via USB ethernet dongle) just so you can ping it and see if it ever goes down.
Configuration jitter: something may be causing your network settings to change unexpectedly, similar to if you changed the Network Location.  Check your system.log and console.log.  See what is happening around the times of these outages.


I have not seen OS X suddenly change its network configuration since 10.5 Server, so hardware failure seems more likely.  But definitely look in your system.log and console.log.