No one wins in a civil war, and no one comes out looking good, siding with the loser can do you lasting harm, better to stay out of it and let it work itself out in the fullness of time. At least until they start gassing civilians. That should lose you any friends you've got left.
Nations such as Lebanon and Jordan really would gain immensely on the world stage if they were to sever ties with Syria. They should not want ties with a country that has a party such as the Syrian Social Nationalist Party gaining so much power. It is a dangerous bunch.
Such as in business, nations often need to be choosy about the people they engage with or do business with, so to speak. if a nations leadership party is unwilling to cooperate or is uninterested in ringing mutual benefits, there comes a time to cut ties when the returns begin to diminsh.
As long as the Syrian Social Nationalist Party exists, I think that neighboring countries like Lebanon and Jordan would gain and benefit from severing ties from Syria. I think that Syria is in such turmoil right now, that no country would gain anything positive from being associate with them in the international world.
Syrias neighboring nations are not considering cutting ties to Syria or their Nationalist Party. They would not benefit from such a move except perhaps gaining support from Nations who oppose the Syrian Nationalists party. They run the risk of alienating themselves from Syria by doing so, and thus limit their access to borders and trade with Syria. It is simpler and wiser to keep things positive with the Syrian Nationalists and just wait out the civil war until someone wins.