I didn't find anything wrong with it, but here's what my events look like.
WebStorage: Local Key "HighScore" exists: System: Set HighScore to WebStorage.LocalValue(HighScore)
System: Else: Set HighScore to 0
System: Score>HighScore: WebStorage: Set Local Key "HighScore" to Score
System: WebStorage: Local Key "HighScore" exists: System: Set HighScore WebStorage.LocalValue(HighScore)
highscore: Set text to "High Score" & HighScore
System: Else: System: Set HighScore to 0
highscore: Set text to "High Score" and HighScore