Typical of cloth tape! It get dirty and fast too, scrubbing it and getting it wet through usually loosens the glue
and it can move, I'd just re-new it.
Other tips are...
keep your hands very clean.
If you use track mitts keep them washed & clean too.
Keep the bike clean.
Carry baby wipes in a tiny bag, these can be used for clean up in the event of a break down or puncture.