Sounds like you need a better computer? As other poster said, you don't *want* to be advancing offline. Killing shardkeepers and suber bosses is FAR more important than stage progression, which means you need to be overleveled. And the easy way to be overleveled is to periodically farm gold (and not progressing) by closing the game for a while.
I've obtained 19 hearts... I've only rebirthed once.
(And P.S. Been a while since I played them, but I don't remember advancing when when the game wasn't running in either attack on Moe or fap titans, the only other games like this I've played.)