For SpaceX there is no drawback to having a brief interruption in the broadcast. The live transmission is for entertainment/PR purposes only, and they're already elbow deep in good PR so don't need any more.
The ASDS stores the video onboard. SpaceX often publishes the landing video later. Even for crash landings, with the stage exploding on the barge, the video recordings remain intact. The video is available for engineering analysis a few hours after the landing, which is soon enough.
There would be a significant cost to making sure the transmission is uninterrupted.
You can't use a buoy. There's a satcom antenna (i.e. a steerable dish) on the ASDS. You'd have to provide a reasonably stable platform for that antenna. So that means a boat or barge.
I've indicated one of the antennas in this image:
There's another on on the other side of the barge. They're pretty big (I estimate about 1 m diameter).
That boat means another item whose position needs to be controlled to make sure it doesn't crash into the ASDS. It needs an engine, an azimuth drive or two. Now the boat needs to be big enough to hold these.
Now, instead of recovering just the ASDS, the crew has to recover 2 vessels after the landing, doubling the workload. You need to tow the antenna boat, so that means another tug.
With all this, you still have a wireless link between ASDS and antenna boat. Can't use a wire (will get tangled in a propeller).
So still a wireless link with a transmitting antenna that will be right underneath a rocket exhaust, and can be interfered with by the landing radar. A crash landing on top of the antenna will still take out the transmission.
So you'll spend a lot for no benefit. This is why SpaceX won't bother improving the live landing feed. Not until large-scale BFR operations become a reality and turnaround time needs to drop below 24h - then SpaceX might benefit from having the landing video available sooner for analysis.