I had that problem with a Cuban Crafters stainless steel perfect cutter double guillotine. I minimized the problem but wetting the cap in my mouth before cutting. Now I use a Xikar V-Cut, still moisten the cap on my tongue before cutting, and very rarely have the wrapper start to unravel.
I think the guillotine cutters cut too deep, removing too much of the cap, which usually holds the outer wrapper leaf at the head of the cigar. You have to carefully insert the tip of the cigar into the cutter to remove only a paper (wrapper leaf) thin slice.
Try moistening the cap and avoid pushing the cigar too deep into the cutter, whichever type you use.
delta1 wrote: