You can try a piece of cardstock as a shim first. Place it between the A plate your cutting plate.
Another thing to try is turning your die face up to cut, and then make another pass die facing down.
If those don’t work, you may want to get a metal shim.
This is the shim I used with my Cuttlebug: https://www.amazon.com/CottageCutz-CCSHIM1-Universal-Shim-Plate/dp/...
I also used cereal box pieces to help shim my machine. I used them when Gina shim hers with cardstock. I had more cereal boxes than cardstock that I wanted to use for a shim.
You can also rotate the die so it is not always in the "shallow" spot.
thanks for the suggestion
I generally run my dies through with a card shim (like the cereal box idea above), then just twist the whole stack about 1/4 turn and run it through again. Mine is usually done by then, but occasionally needs another 1/8 to 1/4 turn and being run through one more time. I've found that a new B plate does the trick without a shim, I just hate to replace them that frequently.