You most likely have a bad TTR in the system . They are a shared resource in the system once the bad one come up to be used again the system will not recognize touch tones until you hang up and make another call. If you have 2 TTRs in the system every other analog call would do as yours does.
In some cases of a bad TTR, once the bad one is being used the system does not even "know" you are dialing because you are dialing to deaf "ears" (TTRs)

Do a TTR Test With 3 - 012 cards you should have at least six. Sounds like a bunch are bad