How can I repair drywall to rehang a heavy rack in the same spot?
You are simply putting too much weight onto the drywall. Options:

Move it so that you are securing to studs in the wall
Remove drywall in large area and add blocks between studs. Redo drywall, patch, sand, paint, and rehang rack securing into blocking
Get a nice wide (atleast 1x4 or 1x6&quot;) board. Cut it long enough to be secured into at least two studs. Ideally, you want it longer by the same amount on each side of your wine rack. Place on wall and screw it into studs (2 screws per stud; 2.5&quot; screws). You can hide the screws with either wood filler or paint depending on the look you prefer. Mount the rack to the board.

There is a possibility that you could hang it with new larger anchors, but we would need to know what exactly you are hanging and what anchoring you are using. If you used little 15lb picture frame kind of anchors, you can probably get the 75lb drywall screw-type anchors and reuse the holes, but not if the rack is going to be 100lbs when loaded.