I've never had both gaffs cut loose at the same time when I was running a saw, but I have had one go now and then. I just did the same things I always do when a gaff slips...lean the other way, and quickly set the loose gaff back into the bole. It never has seemed much of a deal to me. Always keep control of the saw, with both hands. The rest will take care of itself. If both gaffs go, bring a knee up between your hips and the bole, and push back against the bole with the body of the saw to tighten your lanyard.
Before I start to run a saw while on gaffs, I make sure things are all settled and firm, firmer than just when ascending or descending. I make sure I'm not moving around left to right much, not wallowing the gaffs around as I cut. If I need to reposition myself, I set the chain brake and then do so, get all settled again, then recommence cutting. Just stay tuned into your situational awareness. It's not anything to weird out about.