Okay, so back to the topic of the Queen and abdication.
I think the issue of why the Queen won't abdicate comes down to a few things:
1. There is no British tradition of abdication. This is not like in the Netherlands where the majority of monarchs have abdicated. Only 4 English/British monarchs have abdicated - 2 were forced to do so, 1 was pronounced as having done so by fleeing the country, and 1 did so willingly but was then essentially exiled by his family. Mary, Queen of Scots was also forced to abdicate. We would have to go back to the pre-Alfred the Great kings in order to see one who abdicate willingly without negative repercussions.
2. HM was 10 when her uncle abdicated. This is a really influential age, and that crisis had a profound impact on the rest of her life. The Queen was raised by three people who had very strong opinions on the issue of abdication: her grandmother, Queen Mary, who refused to so much as meet the woman that her son had abdicated for, her father, George VI, who was forced to bear this great burden of being a monarch because of his brother, and her mother, HMQM, who would go on to blame the abdication for her husband's death (however wrong she may have been to do so).
3. When HM was 21 she declared "that my whole life, whether it be long or short, shall be devoted to your service and the service of our great imperial family to which we all belong." Essentially, at the age of 21 she dedicated her life to the service of her realms and her subjects. More than 60 years later she has shown that she does not regret this dedication, and just last year she renewed it, saying "I dedicate myself anew to your service...." While she may not have entirely known what she was doing at the age of 21, she certainly did at the age of 86.
4. HM has shown that despite her age she is still very capable of continuing on in her role. She may have had to reduce the number of her engagements, and may not be able to travel as much, but she is still capable of performing the role of monarch. She is still able to do the red boxes, the meetings with the Prime Minister, the state engagements. The rest, as much as we might enjoy them more, are frills that do not have to be carried out by her.
5. It is often believed that by not abdicating the Queen is showing that she does not have confidence in the abilities of her son and heir. This is actually far from the truth. We know that Queen Victoria didn't have faith in her son and heir, the future Edward VII, because she refused to allow him to have anything to do with the ruling of the country. He did not see the red boxes, he did not partake in any of Victoria'a duties. She did not think him capable of ruling and thus did not train him for his future role. The same cannot be said of Charles. He has a part in the red boxes and the official duties. Sure, the Queen has not officially handed him the reigns, but she has shown confidence in his abilities to reign one day because she has taken the time to teach him.
I do think that if there were ever a real demand for the Queen to abdicate, either in favour of Charles (or someone else) or to abolish the monarchy entirely, she would do so. HM governs by the grace of God and the will of the people. If at any point in her reign she has considered abdicating, however briefly, I think it would not be because of a desire to retire or lay down her duty, but rather out of a desire to preserve the future of the monarchy.
