Disclaimer: I'm not a doctor, so I'm not telling you what to do, I'm telling you what I do. Use your own brain regarding your own body.
My forward fall breaks & side fall breaks are decent. My back fall breaks, not so much. We'll have to do high fall breaks at my next Phase, so at a couple of workouts every week, where I have access to a crash pad, I practice them. The goal is to help me get over the fear of falling backward through the air as much as practicing the technique.
So the other day when I was flinging myself to the ground repeatedly like some sort of confused schoolyard bully trying to steal my own lunch money, I managed to whack the back of my head on the pad quite nicely. Not too bad, no little flash of light, but a couple of hours later my neck stiffened up & didn't want to swivel my head around the way it's supposed to. No real injury, just an inconvenient boo-boo.
That night in GB's class we practiced slow sparring & Matt kept grabbing me by my headgear & slinging me backward & forward to headbutt me. I was gritting my teeth because he's already being so careful not to bust open my gut where I had the surgery, so I figured I should just suck it up. However by the end of the class someone yelled, "Stop slinging me around by my damn head, my neck is killing me!". The voice sounded suspiciously like mine - my mouth betrayed me once again. As I listened to his brief by heartfelt lecture about how it's my responsibility to tell my partner these things (shut up, please) I wiggled my head & shoulders around, & guess what? His cruel massage fixed me. My neck felt totally fine.
We get lots of inconvenient boo-boos in Krav. The question is, when do you train through it & when do you stay home & watch Family Guy? For me, the general rule is if its stiffness and soreness from training, more training will make it go away. Go to class. If it's a limb that's out of commission, I have other limbs. Make accommodations for the the injury by protecting it, not using it, etc. Go to class. If there is a risk of making an injury worse so that it will remove me from training completely for a week or more, or if my doctor says, "wake up!" then I'm watching class only, or watching Family Guy.
It can be difficult sometimes to be objective about our own lives and our own bodies, so the goal is to take one's ego out of it. Training when our situation is less than perfect teaches us to endure and to persevere. We can do much more than we think we can, just be smart and don't make a moderately bad situation worse.