persistent

from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Refusing to give up or let go; persevering obstinately.
• adjective Insistently repetitive or continuous.
• adjective Existing or remaining in the same state for an indefinitely long time; enduring.
• adjective Botany Lasting past maturity without falling off, as the calyx on an eggplant or the scales of a pine cone.
• adjective Zoology Retained permanently, rather than disappearing in an early stage of development.

from The Century Dictionary.

• Persisting or continuing in spite of opposition, warning, remonstrance, etc.; refusing to cease or give up some action, course, or pursuit; perservering: as, a persistent beggar; persistent attempts to do something.
• That endures; enduring.
• Specifically— In botany, continuing without withering: opposed to caducous, deciduous, or marcescent: as, a persistent calyx (one remaining after the corolla has withered).
• In zoology, perennial; holding to morphological character, or continuing in functional activity; not degenerate, deciduous, or caducous, as a part or an organ: as, persistent types of structure; the persistent horns of cattle or gills of newts.
• Repeated; continual.

from the GNU version of the Collaborative International Dictionary of English.

• adjective Inclined to persist; having staying qualities; tenacious of position or purpose.
• adjective (Biol.) Remaining beyond the period when parts of the same kind sometimes fall off or are absorbed; permanent; ; -- opposed to deciduous, and caducous.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• adjective Obstinately refusing to give up or let go.
• adjective Insistently repetitive.
• adjective Indefinitely continuous.
• adjective botany Lasting past maturity without falling off.
• adjective computing About some data or data structures: existing after the execution of the program. Remaining in existence past the lifetime of the program that creates it.
• adjective mathematics Describing a fractal process that has a positive Brown function
• adjective mathematics non-transient.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• adjective retained; not shed
• adjective never-ceasing
• adjective stubbornly unyielding
• adjective continually recurring to the mind