[Eliza Shipwrecker]

I often sail solo, and have taken down numerous flag ships using my broadsides without sinking them. I've done it with every type of ship except a war galleon, and have never had a problem. I accidentally sunk a couple using firebrand from the crew cannons before I figured out what was going on, but never with the broadsides.

If it's happening to you every time, you may have something else going on. I would grab a few screenshots with the coordinates, and submit a bug report.