I just had my bottom back molar removed, for an implant at a later date, even after six vials of Novocain (Probably close to 30 separate shots) my tooth would not go totally numb and I felt a very strong localized pain during the removal of the tooth. The doctor said she never has seen anything like it before and that she could not put anymore Novocaine in me. So I clung to the chair and experienced a 8 or 9 pain for a minute or so as she worked it loose slowly (we already determined one huge yank would be way too painful). It actually felt more painful when her steady pull was slowly released, but it eventually came out, yay! Writing this five hours later and I am in no pain now. I'm never nervous at at a dentist and I usually don't even use Novocain when getting a cavity filled, so I'm sort of tolerant of a little bit of pain. Just glad the extraction part is over. This was the first link that came up in a Google search on my curiosity of what I just experienced, so I thought I'd leave my two cents worth of my "fun" for the day.
So, if you're experience is the same (you are not alone!), and the work absolutely must be done, general anesthesia may be the way to go. It's not a great answer, but for someone who experiences this, it may be the only answer.