Greetings and hope I can help!
I bought a 2nd (or 3rd) hand Wilson 1000, worked great for the 1st 6 months after buying it off of flea-bay, but then the SWR kept climbing. I tried to tune it and ended up cutting off almost an inch off the whip with no significat improvement, so I got tired of :bdh: so I stuck it in a closet and it wasn't very happy at all. So, fast forward 6 more months when I was able to pick my CB shop tech's brain. He suggested checking the thin foil that's stuck onto the magnet surface that makes contact with the roof of the mobile it's mounted to and where it connects to the shield of the coax on top of the magnet. Lo-and-behold, it's barely has less than 1/8th " of solid connection from the top of the magnet to the base, the rest of the foil has ripped and is covered with rust. So, had a spare (used) K40 magent that we used for the 1000. Drilled out the rivet that held the shield (-) wire from the coax to the PL259 mount where the coil/whip mount screws into, installed a new ring-crimp terminal, and got a perfect match. If I have the time in the next few days, I'll photograph my K40 magnet Wilson 1000 mod. Hope this gives some ideas and hope you get it fixed. Great antenna BTW
Hank states in his original first post that the antenna is "brand new" so your scenario is not likely and as physco states the Wilson 1k does not have a shunt capacitor which is correct, as far as I know the only Wilson that does is the " lil will" model and it is a pos which I found doing test of my own against the Wilson 5k.
''It" is very possible the the shield does not have a connection do to a defect in assembly at the base and or the SO-239 connetor and he should check that as well as check of continuity from the center pin of the SO-239 to the antenna's whip and from the outer shield to where it connects to the antennas base, failure of one or both will cause this issue Hank speaks of and a break in either.