You can fix the exiting with a while loop:
Code:
bool usercontinue (void)
{
    char DoneCharacter;
    cout <<
       endl <<
          "Continue?" <<
             " - Press \"n\" and \"Enter\" to stop: ";
             cin >> DoneCharacter;
             return (DoneCharacter != 'n'); // true when not "n"
}

int main()
{
        while(usercontinue()) {
	string name, date, action, descript;
	float balance, amount;

	ifstream fin;
	ofstream fout;

	cout << "enter the name of the Checkbook filename: " << endl;

	cin >> name;

	//string update(name);

	//update.append(".update");

	fin.open(name.c_str(), ios::in);
	

	fin >> balance;

	while (!fin.eof())
	{
		fin >> date >> action;
		//cout << date << action;
		fout << date << action;

		if (action == "credit")
		{
			fin >> amount;

			fout << amount;

			balance = balance + amount;

		}

		else if (action == "debit")
		{
			fin >> amount;

			fout << amount;

			balance = balance - amount;

		}

		getline(fin, descript);

		fout << descript;
	}

	fout << balance;

	fin.close();
	//fout.close();
 }

}//end main