Large Language Model-based Multi-Agent Systems represent a promising paradigm for tackling complex problems through agent collaboration. However, the reliance on open-ended communication exposes a fundamental vulnerability: the collaborative process itself can be exploited and disrupted. In this work, we formalize this threat class as Denial-of-Collaboration (DoC). Unlike DoS, which targets individual nodes or services, DoC attacks corrupt the collaborative structure of the system, transforming its communication topology into self-sabotage. The result is excessive resource consumption and eventual system paralysis. We introduce **CO**ntagious **R**ecursive **B**locking **A**ttacks (CORBA) as a concrete example of DoC, which employs benign yet recursively contagious instructions, forcing LLM-MASs into cycles of meaningless message passing. Critically, since our attacks are semantically benign, they easily bypass conventional safety alignments that are not designed to detect behavioral or systemic attacks. Through extensive experiments across diverse topologies and models, we demonstrate that CORBA achieves system paralysis where the baseline attacks fail. Our work reveals emerging DoC threats in current LLM-MAS security and establishes a crucial baseline for developing robust, collaboration-aware defense mechanisms.