How to replace input within a loop

I suggest splitting up the user input part from the checking part.

You could also use the standard library function std::all_of to check that all characters in the string fulfills the requirements.

Example:

#include <algorithm> // std::all_of
#include <cctype>    // std::isalpha
#include <iostream>
#include <stdexcept> // std::runtime_error
#include <string>

// the testing part
bool alphabeticString(const std::string& word) {
    return
        std::all_of(word.begin(), 
                    word.end(),
                    [](char ch) { // a lambda function for testing a char
                        return std::isalpha(static_cast<unsigned char>(ch)); 
                    }
        );
}

// the input part
std::string prompt() { 
    std::string word;

    while(std::cout << "Enter a word: " &&
          std::cin >> word &&
          not alphabeticString(word))
    {
        std::cout << "A character is not alphabetical, please try again.\n";
    }

    // cin is a bad state - extraction of a string failed
    if(not std::cin) throw std::runtime_error("utter failure");

    return word;
}

int main() {
    try {
        std::string word = prompt();
        std::cout << "You wrote: " << word << '\n';

    } catch(const std::exception& ex) {
        std::cerr << "Exception: " << ex.what() << std::endl;
    }
}

You could always call alphabeticString function recursively and return it like this:

if (isalpha(word[i])==false) {
    cout << "Please retry a character is not alphabetical\n";
    cin >> word;
    return alphabeticString(word); 
}

You could split the method:

bool isAlphabetic (std::string word)
{
   bool return_val = true; 
   for (int i = 0; i < word.length(); i++)
   {
      if (!isalpha(word[i]))
      { 
         return_val = false; 
         break;
      }
   }
   return return_val; 
}
std::string string ();
string << cin;
while (!isAlphabetic(string))
{
   cout << "Word is not alphabetic!" << endl;
   string << cin; 
}