Has your Mum checked her bank account/credit card to see if they took the premium? If they did, then she needs to kick their a*ses and you should have been covered. If not, all may still not be lost since they have a direct debit and it could still be their incompetence that they didn't renew. Or was the direct debit refused because of lack of funds (in which case someone - bank or ins co - should have told her).
Keep on at the company, they do make mistakes and this one could be serious for you.
There is a moral to this story - never throw out a letter like this from the insurance company (amongst other things, it must have told her how much they would be extracting from her bank account. Also, in phone conversations, always note the date and time and the name of the operator you're talking to. Try to get their surname too, because "Susan" could be one of many operators with that name!
Finally, since "calls may be recorded and monitored for training purposes", try to get them to dig out the recording of the phone call where your Mum was told she was still covered. I bet they've conveniently lost it!
Finally finally, insurance companies don't write to tell you a policy has lapsed.