There's no possible way that not shutting down properly could result in losing several levels. In fact, there's no way that not shutting down properly can lose you more than a few hundred exp and that's only assuming that your computer shut off in the middle of an exp party, or you shut off while a mob is attacking you causing you to have a dead character when you log back on.

But based on everything I know about FFXI, what Tsukasa says happened to his character could not have possibly happened.