persistent

Obstinately refusing to give up or let go.

Insistently repetitive.

Indefinitely continuous.

(botany) Lasting past maturity without falling off.

(computing) Of data or a data structure: not transient or temporary, but remaining in existence after the termination of the program that creates it.

(mathematics) Describing a fractal process that has a positive Brown function

(mathematics, stochastic processes, of a state) non-transient.