The Queen's recent speeches concerning her Jubilee have made it pretty clear that she does not intend to abdicate, and will reign until she dies, unless The Revolution comes first of course - death duties debate anyone?
As death duties are paid to the state, and the Queen is the state that would be like a scorpion stinging itself. I suspect that given the bad experience with her father the old trout will die in harness. re the death duties thing...all her state holdings are in trust anyway.