The wreck was not far off Beechey Island, and its general location fairly readily ascertained. The first definite evidence of the wreck was located by diver Joe MacInnis in 1975; based on his evidence and subsequent searches, a Canadian Coast Guard vessel discovered the wreck using side-scan sonar in 1980. Remarkably, her hull was largely intact, and two of her masts will still standing, one of which still seemed to be carrying some portion of canvas. MacInnis later led several dives to the wreck, and retrieved the ship's wheel. This and his earlier searches were described by him in his book The Breadalbane Adventure, which featured an introduction by Walter Cronkite.
MacInnis later hit on the idea of setting up a seasonal camp on the ice, and taking aquatic tourists down to the wreck at thousands of dollars a pop. To that end, he purchased a number of large mobile dwellings, had them shipped to Resolute, and fixed to skids so they could be towed out onto the ice by tractor. The hoped-for number of tourists never materialized, and when I was at Resolute in 2004 the mobile units could still be seen, abandoned, a few hundred yards from the main port.
You might think that all the archaeological knowledge possible had already been retrieved from the Breadalbane, but this didn't stop Canadian Forces divers from searching the wreck again this April. The annual northern military exercise in Nunavut, though it mostly involves staged search-and-rescue operations, is also geared toward strengthening Canada's claim to its northernmost territories, and apparently nothing spells "sovereignty" quite so well as a sunken Franklin-era vessel. Nothing new was discovered, so far as I know, though the online video shows some intriguing images. There's also a fairly detailed account of the dive on the Canadian Forces' own website here.