I'm going to take a stab at this, with the following caveat from the Porter Cable manual:
For your continued safety and electrical protection, brush inspection and
replacement on this tool should ONLY be performed by an AUTHORIZED
PORTER-CABLE SERVICE STATION or a PORTER-CABLE•DELTA FACTORY
At approximately 100 hours of use, take or send your tool to your nearest
authorized Porter-Cable Service Station to be thoroughly cleaned and inspected.
Have worn parts replaced and lubricated with fresh lubricant. Have new brushes
installed, and test the tool for performance.
Any loss of power before the above maintenance check may indicate the need
for immediate servicing of your tool. DO NOT CONTINUE TO OPERATE TOOL
UNDER THIS CONDITION. If proper operating voltage is present, return your tool
to the service station for immediate service.
Having read their advice, also take a look at the diagram of parts in this link http://www.dewaltservicenet.com/Products/DocumentView.aspx?productid=14279&typeId=11221&documentId=30477
and see whether you feel comfortable disassembling something like this. You probably won't have to tear into the motor housing, but if it look dicey to you,please go to the home page of that same link and find a service center near youto do the work.
With that in mind, consider the following. I have the same sander, and have used it as one of an arsenal of sanders for many years. I think I remember having an issue like you describe, about ten years ago. Now if I can only remember what I did to repair it.....just kidding.
It's possible the bearings are worn out and need to be replaced. In that case, you might be better off having it serviced by a professional shop who can also replace worn brushes and clean and lube it to factory specs.
But it's also possible that the screw that mounts the metal pad to the bearing (#114 in dwg.) has come loose. I think that was the case with mine, and it was not the same sander, it vibrated so badly. I remember having a definite reason to tear into it, and I needed it for a job.
You might be able to access this screw by lifting a flap of the rubber pad and removing a dust seal, but if you feel adventurous, remove the four screws that hold the felt or rubber pad on the base of the sander. Be careful, because if you're not very careful you may have to replace this pad. (It should be readily available for a few bucks somewhere local, depending on your location.) In my case I made a custom cork bottom pad that was a bit stiffer than the foam rubber to keep my sanding sheet flat, but that's another story.
If you get this far, check to see that the center screw hasn't vibrated loose. If it's in tight, you need to check for play in the bearing that the metal base (#127, bearing & pad holder) is mounted on. If that bearing goes, the works will vibrate. Replace it if you can detect any play at all between the center race and the bearings. I'd change it out just for good measure if you have used the tool a lot.
Put everything back together carefully, tightening all screws with the right driver. And hope for the best!
I hope this is the solution to your problem. If you need parts, consult the web site listed above. They should be able to sort you out. Good luck! Let me know how it works out, or if I can help in any other way.