Do you believe Romans 11 is teaching that a person can lose their salvation and then regain it or that they can gain salvation and then lose it?
No, I explained that twice now. I don't believe that the tree represents salvation. I believe it represents God's revelation. Israel was chosen to receive the special revelation of God (via prophets, commandments etc). Now, the special revelation is going to the Gentiles (via the apostle...the gospel).
Israel is being cut off or blinded from the gospel, which means they are cut off from the tree. The tree is the means that a branch gets water and nutrients and for years that was going to Israel, but now it is going to the Gentiles.
So, to be cut off from the special revelation of God doesn't mean you loose your salvation, it means you stop getting his revelations. To be grafted back into the tree means that you can see, hear, and understand God's revealed truth. This truth is the means through which men come to faith.
This is why I have a problem with the idea of thinking of the tree as meaning salvation itself, because it leads to the problem you are having where a group of people (made up of individuals) are being cut off from being saved and grafted back into being saved. That just doesn't work. If, however, the tree is seen as the MEANS through which salvation comes, you don't have that problem.
If that is true, then we disagree. The passage was not intended to teach such a thing.Paul's hope is for the Jews, generally, to be grafted back into the tree at some point in the future.... when the fullness of the Gentiles has occurred. He doesn't give a specific time for that.
No he doesn't, but he certainly seems to think there will be some of those hardened Jews who come to faith as a direct result of his ministry.