Obstinately refusing to give up or let go.
She has had a persistent cough for weeks.
Insistently repetitive.
There was a persistent knocking on the door.
Indefinitely continuous.
There have been persistent rumours for years.
Lasting past maturity without falling off.
Pine cones have persistent scales.
Of data or a data structure: not transient or temporary, but remaining in existence after the termination of the program that creates it.
Once written to a disk file, the data becomes persistent: it will still be there tomorrow when we run the next program.
Describing a fractal process that has a positive Brown function
(stochastic processes, of a state) non-transient.