Joseph A Bank was sued for perpetual sales [1]. The case was dismissed for defects in the plaintiff's case unrelated to the legal theory (they couldn't produce receipts of their supposed purchases), but of course even an unsuccessful lawsuit of this nature could bankrupt a startup.

Of course, without deep pockets, a startup is also unlikely to be targeted for this.

1: http://business.time.com/2012/06/11/can-you-sue-a-store-for-...