Indeed.
My 3/4 hp SuperPump will sometimes slow to a crawl, then to nothing and the pressure will also drop off to almost zero. It usually happens when the the draw is loaded up, like a clogged filter basket from vacuuming, or debris around the drain combined with the flow being diverted to either (plus the 40' run from the pool to the pump). The pump goes into a cavitation condition for which the only solution is to shut it off and turn it back on again. Clearing the obstruction allows me to continue vacuuming, or the drain to keep flowing, without interruption.

OP states the pressure jumps up when he starts. So does mine, so do they all. But jumps up to what? He also states it happens whether there's DE or not and that he's completely cleaned the filter. The question then is: when the flow slows, does the pressure drop off as well? Remembering the pressure reading is the backup of water the pump is trying to push through the filter medium, this would clearly indicate the pump is being starved to the point of cavitation, the operative being 'starved'. And cavitation doesn't occur immediately, it can creep up over five to fifteen minutes This, to me clearly indicates a partial obstruction somewhere on the suction side.

Of course if the pressure is maintained as flow drops off, then nevermind.
: )

To CarlD's point: I think it's more the pump is too big for the amount of water capable of being supplied to it. It can't overcome the losses on the suction side, and cavitates. I'm betting he has 1- 1/2" lines.

C.