I sometimes loose water pressure sometimes to a dribble from both hot and cold water.I have a single faucet with a single off,on value.I took the hose connected to the faucet head apart and noticed little white balls similar to small white styrofoam you find a packaging.I cleaned it and my water pressure returned,but after awhile it happens again and I have to take it apart again for the pressure to return.What is this?How can I eliminate this from to happening?

I suspect as deteriorating dip tube in the water heater.

Also, if those pieces are perfectly round and you have a water softener, have it checked out. Ours were a different color but the general description sounds similar. Regardless of the source, make certain that you are not drinking water from a faucet that doesn't have a screen as these unidentified materials can clog the kidneys as well.