Vermont, queen singing is called piping. I think I spelled it correctly.
I have listened to many a queen piping but only upon introduction or hatching. My understanding is piping is a Queens way of saying HERE I AM. Any other queens in the colony would respond accordingly.
To answer your question of why the queen is piping for weeks is not understood by me. If there is any trace of OLEIC ACID, queen pheromone, on your gloves or clothing, this would trigger piping. If the queen only pips when you open the hive then I would conclude somehow you are triggering.
The chemical name of oleic acid is: 9-oxo-2E-decenoic acid, probably more than you wanted to know. However this chemical is a fatty acid commonly occurring in olive oil, vegatable oil, and many kitchen type oils,,,perhaps you contaminated your hive tool, gloves, or whatever with these oils.
I know queens are very active to this pheromone. Case and point: queens are known to be handled without gloves and they rarely sting. I hold queens in my bare hands to be marked. However I now only handle one, because I got nailed right in the finger tip upon holding queen number two. You see, when I handled the first queen, she marked me with her pheromone, when I grabbed the second queen she responded to the queen pheromone and nailed me. So now I keep alcohol to remove any scent on my fingers or I just handle one queen.
Blessings