According to Romans 11:25, “For I do not wish you to be ignorant, brethren, of this secret — that ye may not be wise in your own conceits — that hardness in part to Israel hath happened till the fulness of the nations may come in;” (YLT). Surely, if the fulness of the nations (or gentiles), will come in before Israel comes to Christ, there can be no salvation for the gentiles after the rapture.
Romans 9-11 have to do with the Church and Israel. In that context the place the Gentiles come in to in Romans 11:25 is the Church. The Greek wording of the verse actually implies that the partial hardening of Israel’s heart will continue until the Church reaches its intended destination, which is the New Jerusalem.
At the Rapture, the church’s number is complete, but gentiles will be saved through out the Great Tribulation. This is confirmed in Acts 15. In verses 13-18 James gave us the sequence. First the Lord will take from among the gentiles a people for Himself (the Church). Then he will rebuild the Temple in Israel so that the remnant of men may seek the Lord. Notice that he spoke of Gentiles seeking the Lord after the Church is gone and after the Temple is rebuilt. Since we know that a Temple will exist during most of Daniel’s 70th week, it’s clear that James was referring to the time of the Tribulation.