ok, then the next step is to not input int, but input strings insteads, this way you won't get the failing stream on char inputs and you'll be able to test the whole input before passing it on.

Code:
//Written By : Andrew Bomstad and Darryl :-)
//"Day6"

#include <iostream>
#include <cctype> // prefer cctype over ctype.h
#include <string> 

#define cls system("cls");
#define pause system("pause"); // ok for newbie but ditch it with experience

using namespace std;

int main()
{
	while (true)
	{
		cls
			string input; // c++ strings are your friend.
		bool valid_input;
		do
		{
			cout << "enter a digit : ";
			cin >> input;
			// don't need the cin check now
			for (int i = 0; i <input.size();++i)
			{
				valid_input = true;
				if (!isdigit(input[i]))
				{
					cout<<"Error: Non-numeric data entered\n";
					valid_input = false;
					break;
				}
			}
		}while (!valid_input);

		cout<<"You entered the number "<<input<<endl;
		pause
	}
}