The OP was never eligible for registration (which ended with the 1977 Act) or the special grant of citizenship from the 1977 Act (if that is what you are referring to). If the OP's grandmother became a US citizen as a minor when her parents became US citizens, she would have lost her British subject status and did not become a Canadian citizen with the commencement of the 1947 Act; I think this is the most likely scenario. However even if it is not, British nationality law at that time (as well as the 1947 Canadian Citizenship Act) did not allow married women to transmit their status to their children, or to allow birth abroad registration for said children. The 1977 Act was not retroactive to the applicant's date of birth, so even if the OP's parent was able to apply for it, the parent would only be a citizen from the day on. The OP would not be able to apply under the special grant because his/her parent was not a citizen until at least 1977, and the OP was born in 1962.
Ok, so by calculation his parent (the child of that grandmother) was born before 1947 (given he was born on 1962, his parent would have been only 14 years old or younger if he/she was born on or after 1947). So most likely that parent was born before that.
With that said, there were other ways for children of British mothers to retain their citizenship
So with that said there are some more important questions there:
1. What was the citizenship of father of that child at the time of birth. Especially if his grandfather was British at the time his parent was born. (because all she needed not to loose Canadian citizenship in 1947 was not to loose British before, so marrying a British subject abroad would have been enough).
2. Was that child born out of wedlock or not. Because if not that child would become Canadian by descend by 1947.
3. Was that child his mother or his father. And if it was mother, what was the status of father (especially regarding possible dual citizenships (like British for example).
So yes there are technically several options when he could have inherited that citizenship, but because of the failed registration he would have lost it.