This URL might provide the info you are look for. Its for the Catalyst 3750, but the URL is also listed on the Catalyst 3560 troubleshooting page.
I've also found this URL which might give some additional info https://supportforums.cisco.com/thread/161063
We had the same issue with two 3750Es (WS-C3750E-24TD) running c3750e-universalk9-mz.122-55.SE1.bin, same thing in standalone and stacked. Even after pushing those into a stack of 3750Gs (WS-C3750G-24T) the utilization was essentially the same. No performance issues have popped up, so we haven't put too much time into it. Have you tried disabling the ports as the Support Community suggested?
I am guessing you haven't been running those 2960's for very long. If you had, you would be running and screaming from that code=)
The version of code you are running has a signifigant bug in it where after about 6-8 weeks of uptime, you can expect some pretty signifigant packet loss. It goes away as soon as you SSH into the device so it will look clean but once you log back out, it will go right back to packet loss.
Version 12.2(55) and above fixes this bug.
My colleague was experience similar problem on C3750X.
But the problem is most 12.2(55)SE and 12.2(58)SE releases are listed in the known affected versions.
Personally I run a couple of C3750X with the latest 12.2(58)SE2 without experiencing this problem.
You may either try out 12.2(55)SE4 which just release 1 month ago and not listed in the affected versions, or try out 12.2(58)SE2.
I always avoid IOS 15.x releases. Cuz already had a few hard-time with them.