I just got a Da Vinci Mini for Christmas and I think everyone has this problem right out of the gate. The good news is, it’s a pretty easy fix.
When you apply the square tape, you then need to do a quick coating of Elmers Glue stick on top of the tap to help anchor down the first few layers. I didn’t see any distinction in what kind of glue stick, so I just went with the Elmers All Purpose, which worked great. However, I have read subsequently that you might want to use the washable stuff that is purple instead.
I will say that once I cleaned out the first couple of disasters, and got the glue stick down, the rest of my prints with complicated threaded parts came out perfectly. I also recalibrated before every job.
Give it a try. Good luck.
PS - The Mini can only do PLA, for now I’m told.