It seems you've figured that the real consequence of skipping a day is losing motivation for the next day, rather than a loss of improvement. The number I've heard for how long before you actually start to lose any gains you have made is 6 weeks, so if you get really bogged down for a week apartment hunting, you can get back into it almost where you left off. As long as you get back into it. That's the hard part. For the burpees, I'd say break them into sets. They exist in this odd category as a mostly anaerobic cardio exercise that require a certain level of strength too. So, like sprints or strength training, I think it would be perfectly reasonable to keep breaking them into sets.
I did; they still seem freaking hard. I suppose they're meant to - per aspera ad astra - but right now, they feel too hard to pursue. Like I said in the post: I get a certain level of endurance and strength for each consequent day, while with burpees, all I seem to do is challenge myself. It might very well be that I've picked the wrong challenge for me: while Running and Core Challenges work slowly but steadily towards the goal and I get the feeling that I can tackle the next one since I did all the previous ones, Burpees Challenge just tires me physically and mentally. If I decide to drop it - which seems more and more like a reasonable idea - I can always pick it up later, or include them, in a different fashion, in further challenges, or leave it on the floor and, instead, take up something that suits me more.For the burpees, I'd say break them into sets
I think part of the reason you're finding the burpees especially tough is that you are doing them last after both running and pushups earlier in the day. Basically, if those challenges are pushing you well, the burpees may be overkill. Getting rid of them may actually help with the other Challenges.