I don't necessarily have a problem with retaking, but it can have some downsides. For example, by providing a safety net it might discourage adequate preparation for kids that are already becoming lazy.
With regard to the 50% floor, I initially had objections based on wrecking the grading curve. But since I guess even a 50% would usually have to be balanced by a number of good grades (assuming that a 50% student isn't likely to turn in an immediately subsequent 100% performance on the next test), I can see the value in not discouraging students by feeling it's impossible to recover after one or two dismal performances. And especially if a 50% grade were averaged with a retake grade, it wouldn't represent a terribly unfair advantage for a student who just didn't get the material the first time.
I'd be most likely to be okay with the scheme if the implementation included some other safeguards, such as two retakes and/or 50% grades triggering mandatory extra work with a tutor. That would make sure that struggling students got more help and oversight, and discourage laziness.
