I have a 3yo 3560 that started sporadically dropping connections. The only configs made to this device were adding an ip for the management interface and adding a vlan. It worked like this for quite some time until recently. It started randomly dropping conenctions to different ports. Everything always showed up/up and reliability 255/255 when I looked at it. Environment looked good to. Load rarely passed 10%, I pulled it and replaced with 2 24ports and the issue stopped. Would reflashing this device help, or does this sound more like a hardware issue?
I would start with IOS and see if there are any known bugs that can cause it to operate this way. Some times an IOS upgrade can fix the problem before changing the hardware.