I too use the Off-Shore brand of planer boards. I have lost fish on the disconnect but I can’t say it has been alot. I use them primarily for crankbaits, or an occasional crawler harness(multiple hooks). I always make sure that the hooks on my cranks are super sharp, typically the factory ones don’t get it done for me, so Owner or Gamagatsu are switched out to fit the bill. I use 10lb Berkly XL, and one thing that I have noticed when I remove the board, with mono (anywhere from 60-180 ft.) you get a little stretch when the fish is pumping, kind of cushioning the head-shakes and runs that the fish is making. Normally the rod’s action handles those fish movements. I fully endorse the use of super lines (Power-Pro), in fact I use the 2/10 on my inside rods not attatched to the boards.
The other thing I don’t do, unless I know the fish is massive, is stop the boat. I imagine with one line out the habit is to throw the motor in neutral. I usually have multiple lines out, so I don’t even slow down. I also will wait when I see a board go off, sometimes until the board has been pulled straight behind the boat.
Your other option would be investing in a boom and some double boards. In combination with the proper weight release clip this system is far more efficient than the clip on style. The best part is after a fish, you just grab another clip and send it out. The boards never have to come out of the water.
With the limited stretch of the Fireline it is quite possible your fish are shaking the hooks, or depending on how big they are, tearing them out.