The Nimukei Yosef cites a Ritva, who quotes the following Yerushalmi: A person will only have the ability to prohibit something presently in his ownership, and the prohibition will remain even after it leaves his ownership. However, he cannot initially prohibit the item only for the time after it leaves his possession.
The Haflaas Nedarim explains: The only reason that someone would have the ability to prohibit something presently in his ownership, and the prohibition will remain even after it leaves his ownership is because it is similar to hekdesh. Since the item in question is presently in his possession, the neder takes effect and the prohibition remains on this object forever just like hekdesh. However, one does not have the ability to consecrate an item that is presently not in his possession, and therefore, a neder to prohibit something only for the time after it leaves his possession will not take effect.
The Korban Nesanel asks: Why couldn’t this inquiry be resolved from the Gemora above (42a-b) which concluded that if one says to his fellow, “These possessions should be forbidden to you”; if he vowed prior to shemitah, he may not enter his field and he may not eat from the fruits which are growing on the branches outside of his field even when shemitah arrives? This is because a person has the ability to prohibit something presently in his ownership, and the prohibition will remain even after it leaves his ownership! Shouldn’t the halacha be the same in our case where he sold the property to someone else?
He answers that shemitah is different. Since the vower has the right to acquire the fruits that are growing just like anyone else, it is regarded as if it is still in his possession, and that is why the fruits remain forbidden. (This is a tremendous chiddush that something can be considered yours because you have the right to acquire it.) However, the Gemora’s inquiry here is regarding a case where he sold the property. In this case, the item is not in his possession at all, and perhaps, the prohibition will not remain after it leaves his possession.
The Shitah Mikubetzes answers that Avimi did not know the conclusion of the Gemora above and that is why he made this inquiry.