Indefinite play becomes possible around 160 or so. At that point you have so many balls you can't really lose. I got to 185 before I got bored. Also, a bug: if you end the game by pressing "skip" and quitting, it doesn't give you a highscore.
You could make this game ten times better by saying something like "you were killed by 'cho' (チョ)" when you die. It's kind of useful for practice, but it sucks having to look up the ones you couldn't remember all the time.
Hi, thank you for the suggestion! Actually, you can roll over the level icon in the top left corner to see the recent characters that killed you or characters that you got a mistake on.
Starting the mission again wouldn't be so bad if you didn't have to sit through all the unskippable dialogue every time as well. The last level is the worst - sit through dialogue, instantly get killed, sit through dialogue, instantly get killed, repeat...
Thank you for reporting this! We'll look into it.