As CornGolem notes, the edges of pieces of tape are not your friend. I recommend using the widest tape that you can find, and wipe it down with isopropyl alcohol before you start printing. That seems to help with both the adhesion of the print to the tape, and tape to the bed.
I don't know about other types of tape - but 6"-wide Scotch 2090 Blue Tape treated with alcohol will hold down perfectly pretty much any PLA print that I try.
You may also want to not use the fan for these prints - just set a nice slow minimum layer time, such as 10s.
If the corner is near the edge of the tape strip then it's going to warp a lot more than if it was in the middle of the strip. Masking tape is made to be removable, so it doesn't stick that well.
You could try printing anchors (helper disks).
Or get rid of tape and use hair spray (must contain vinyl) but in this case it will stick so well that you risk breaking your part during removal (talking about this I'm interested in solutions).
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