I sincerely apologize for the issues you are having with the key verification system.
To explain what is happening: In the current Early Access build, the key verifier is failing to write and save data locally. This means the game doesn't 'remember' you've already activated it, so after you play the game and quit, it'll ask for the key again. Since the system sees the key as already used, it unfortunately prevents you from entering the game again. :O
We have already identified the fix, and a new update will be uploaded this Monday to completely resolve this problem.