Think

Your mother is at the ripe age of 82 who is well acustomed to live alone.She is independent enough to live alone now,may be when she needed you most probably between the age of 50 and 60 you might have not been beside her,busy with your work&family.Now she would not like to disturb you further knowing fully well that her son is busy with his family&job.Correct me if am wrong,this is just a feeling.

no thats not the case here. But you cant know the story.
In fact when I was 22 I returned to my mother and lived 9 years with her. It was a nightmare because she treated me like a little kid and not a grown up person who earns her own money. You wouldnt believe which silly things she was always arguing and making a row about. So when she was about 50-60 I was with her. In fact I moved out when she was 68.
When I was 31 I moved into my first own place a little late, huh? It was only 15 minutes per bus to her house but when I popped in, be it with telling her I would come or not telling her she says why do you come here I can cope on my own. When I phoned she said what do you phone for I am perfectly capable of taking care for myself.
Whenever I asked if I could do something for her she said no.
I have never neglected my duties as a daughter. Now as I am further away she values more when I call or even come to see her what we just did today as I am on vacations and its my aunts birthday today.

She will still stubbornly refuse to be helped.