They give you a lot of excuses for not doing it but never actually say they won't do it.
Stalling could work here:
to delay, especially by evasion or deception.
I asked him to do it, but he keeps stalling.
To procrastinate means to put off, so it could work, too, in some circumstances.
There are many other synonyms, each with different nuances of meaning. Thesaurus.com presents many choices.
Dragging one's feet is another such phrase.
hem and haw hesitate; be indecisive : I waste a lot of time hemming and hawing before going into action.
ORIGIN late 15th cent.: imitative.
Temporize would work. The OED defines it thus:
†2. intr. To let time pass, spend time, ‘mark time’; to procrastinate; to delay or wait for a more favourable moment.
Dawdling could be appropriate here, especially sense (2): to move lackadaisically
I would call the action of someone not doing something for me quickly, simply delay. But if, over time, lots of excuses are given for not doing it, but "Not going to happen" is never said, I would call that being strung along, or being taken for a fool, or messing with my head, depending on what motives I attribute the delay to. (The previously-mentioned stalling, temporizing, and foot-dragging are other terms I might use, but my primary choice is being strung along or stringing me along.)
I'd probably call it inaction.
Not to put too fine a point on it, pain in the arse.