To stretch things a little, and to bring them into the 21st century, what about it being a target of a terrorist attack? The war on terror could be brought to the deck of the Constitution the same way Canada's war memorial was attacked in 2014.
There is airport-level security required to get onboard the ship nowadays, so that's going to make things difficult. Maybe a small plane loaded with as much explosives as possible? That could do some serious damage, if not sink it, although the Constitution is not a big target like a building is. Or maybe a USS Cole-style attack might work.
You've never seen the climax? Bruce Willis has charged the battery & lets loose a broad side from both the 24 pounders and top deck carronades into the villains command post mega van on the dock. In slow motion the dozens of cannon balls scatter the high tech equipment & vehicle in fragments across the late night waterfront.
Do the terrorists take over the USS Cassin Young a few hundred feet away?