One problem I notice with a lot of bar tape is that it has adhesive backing. This adhesive gives the false sense of security that it is helping hold the tape to the bar. Eventually, the adhesive acts like a lubricant.

Use tape that does not have adhesive backing or use some solvent to help remove it.

Also, strange as it seems, I have had good luck lubricating the bars with WD-40 before wrapping. The WD-40 dissipates and the tape is on firm in about four hours. This is an old trick for grips, of course, and I found it also works for bar tape.