He has no significant base of popular support (unlike Fayyad, who has absolutely no popular base of support), so the entire argument for him to stay in power (well past his expired term of office!) is that he is an effective collaborator and is best positioned to serve US/Saudi/Israeli interests. Unfortunately for him, he gets no respect for this service: constant abuse and veiled threats on his position and life from both ends.
By threatening to resign, he is forcing loud-mouths like Netanyahoo and Lieberman at their word: if you think you could do a better job, have at it. At the same time, he dangles the threat of Hamas being without any real competition in the West Bank either (following the total loss of collaborationist power in Gaza after the failed coup attempt by Dahlan and his US/Israeli mercenaries). Well, Abbas is too accustomed to the comfortable lifestyle that is reaped from the rewards of being a corrupt collaborator and patron of Gulf largess, so he has no intention of actually doing so.
Such futile gestures as this and the stunt at the UN are the only real cards he has, counterfeit and well-marked though they may be. Attempting to force the zionist regime to the table for "peace talks" (a cruel, Orwellian euphemism for "what part of Palestine do you want me to surrender today?" , while at the same time utterly decrying the process as a total failure? I'm not sure where they're going with this, not quite sure they do as well. The grand strategy seems to be some variation on the dual theme of "keep Hamas at bay" and "keep the Gulf money flowing", anything beyond this is probably nothing more than ad libbing writ large.