The rules for any resolution state that it must be affirmed by at least 9 out of 15 members of the UN Security Council, but that any of the 5 permanent members (US, UK, France, USSR/Russia, China) can veto it.
Now, I believe most resolutions that are rejected don't have the support of all the permanent members, but I can't really find a list of all proposed and rejected resolutions.
So, has there ever been a situation where the 5 permanent members were all willing to accept a resolution, but the resolution was nonetheless rejected because not enough of the non-permanent members voted in favor of it?