问题就在于执行一次循环之后inFile文件流已读到文件结束处，之后流就处于错误状态不会正常工作了。因此每一次循环之后必须清除流的状态，使其复位。文件流的打开和关闭也必须放在循环中：
#include<iostream>
#include<fstream>
#include<string>

using namespace std;

int main()
{
    ifstream inFile;
    string ans,F,L,firstname,lastname,firstName,lastName,number;
    do
    {
        inFile.open("phonenumber.txt");//文件流的打开放入循环
        cout<<"Enter the firstname and lastname you want to look up:"<<endl;
        cin>>firstname>>lastname;
        
        do
        {
            inFile>>firstName>>lastName>>number;
            
            if((firstname==firstName)&&(lastname==lastName))
            {
                cout<<firstName<<"  "<<lastName<<"  "<<number<<endl;
                F=firstName;
                L=lastName;
            }
        }while(inFile);
        if(F!=firstname||L!=lastname)
        {
            cout<<"The name is not in the telephne directory"<<endl;
        }

        cout<<"Do you find it again?(Y/N)"<<endl;
        cin>>ans;
        inFile.close();//文件流的关闭放入循环
        inFile.clear();//清除流的当前状态，恢复为有效状态
    }while(ans=="Y"||ans=="y");

    inFile.close();
    
    return 0;
}