The Shulhan Aruch (Orah Haim 206) addresses the case of a person who recited a Beracha over a fruit, and then, before he had a chance to eat the fruit, it fell from his hands and either rolled away or became inedible (such as if it became dirty). Should the person eat another fruit that he has with him, relying on the Beracha he recited? Or was the Beracha limited to that specific fruit, such that the person must now recite a new Beracha if he eats another fruit?
The Shulhan Aruch rules that the individual in this case must recite a new Beracha if he eats another fruit. What’s more, the Shulhan Aruch writes that even if the person had several pieces of fruit in front of him which he planned on eating, nevertheless, once he cannot eat the piece upon which he recited the Beracha, he must recite a new Beracha. Even though the individual had in mind for his Beracha to cover all the fruits, nevertheless, he must recite a new Beracha, since he cannot eat the particular fruit over which the Beracha was recited.
However, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) cites other Halachic authorities who disputed this ruling, and maintained that if one was planning to eat other fruits, then he does not repeat the Beracha in such a case. And even if the person had no particular intention when he recited the Beracha, and did not specifically intend for the Beracha to cover other fruits, nevertheless, according to some Poskim, he may eat other fruits without a Beracha in this case. As long as he did not specifically intend for the Beracha to apply only to this particular fruit, the Beracha covers other fruits according to this view. The Ben Ish Hai therefore applies to this case the famous rule of "Safek Berachot Le’hakel" – that one does not recite a Beracha if it is uncertain whether it is required, and so one should not recite a Beracha over the other fruits in this case. This is also the view of Hacham Ovadia Yosef, in his Halichot Olam.
Summary: If a person recited a Beracha over a piece of food, and before he ate the food it fell and rolled away or become inedible, he can then pick up another food requiring the same Beracha and eat it without reciting a Beracha. As long as he did not have specific intention for the Beracha to cover only that particular food, it covers other foods requiring that Beracha, and he can eat another piece of food without repeating the Beracha.