I'm also experiencing this issue, nearly every time. I wasn't sure if it was just my computer, but from this, it sounds like that's not the issue. It would be better if there was some sort of built in save function so you can save your progress as you record your lines. I was almost 10-20 minutes into a recording and lost all of it because of this issue. Super frustrating!
However, I love this concept for a game and I have a lot of fun doing funny voices, so I'm excited to see where this goes, since it's still in testing!