Yes, I do know this problem, and I also found a solution, that helped me:
I've found out that every (new) Zippo, that refused to light, had the same problem: the wick in the cotton runs along one side of the Zippo only, and apparently doesn't get soaked enough.
Take out all the cotton, and start laying the wick in an "S" shape from left to right, with cotton between the curves. So it's one layer cotton, curve and lay the wick all over that cotton layer to the other side, cotton on top of that, rinse and repeat till all is in place again.
Doing this, I've never had any lightning problems with my Zippos again, and they pretty much always light with one strike. I hope I explained it well enough with my wonky english

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And
"I need to do it about every four to six weeks or so. "
Huh!??? I'm workin on 2 1/2 years and my wicks fine.
Dan
Same for me, my Zippo with the pipe insert works for more than a year now, didn't have to trim yet.