The touch-tone is sent from the base unit, not from the individual handsets, so this would be happening with all five of your handsets.
You say it suddenly started happening. The first thing to rule out is to determine if your phone system is indeed sending a touch-tone. Maybe it got switched to the old fashioned pulse dialing. You can test this by calling a friend. Or call your cell phone. Press some keys and see if the tones are heard on the other end.
If the above test is inconclusive, then I would recommend that you call your phone service carrier and ask if they changed any equipment recently. One guess is that they installed equipment that is not allowing the touch-tone to go through to the other end. Another guess is that the touch-tone is not loud enough to be properly deciphered by the automated system on the other end. Discuss these ideas with your phone carrier and see what they say about it.