The heart, arguably the primary target of cardiovascular training, is technically a muscle. While cardiac muscle is quite a bit different than skeletal muscle, significant stressing of the heart (typically considered to be either greater than 85% or greater than 90% of your calculated maximum heart rate) can result in both positive and negative effects on the structure of the heart depending on the intensity and duration of exercise. Though not as well understood as the recovery of skeletal muscle, the heart does benefit from recovery time. My understanding is that it doesn't need to recover from low intensity exercise, but it does from high intensity exercise.
Most people are not at risk of exercising too much. For your situation, an important question is: how high is your heart rate getting? For some people, doing 50 burpees as fast as possible might not exceed 70-80% of the max heart rate, in which case it's almost certainly healthy for an individual without health issues to do every day. If your heart rate is getting really high, greater than 90%, you might want to consider taking a day off in between to get two sleep cycles in to insure you have lots of time for your body to repair your heart/arteries.
The general guideline I follow based on prior research I've done is to limit my time with heart rate greater than 85% to less than 40minutes per week cumulatively. This is pretty easy to do, because keeping your heart rate that high is not something you're going to do on accident. If you're a serious athlete you may want to exceed this limit idk. But as far as lower intensity training, like 60-70% max heart rate, you can pretty much do that 5 hrs a day 6 days a week if you don't have any health issues.
It might be interesting to get a heart rate monitor if you don't already have one to track changes in your HR throughout your burpee workout. This could better help you determine the appropriate recovery time.
