Batters go through slumps, and so do law firms. But some losing streaks are more consequential than others.

In the past six months Cleary Gottlieb Steen & Hamilton litigators have lost a string of historic cases for clients Russia, Argentina and Google Inc., including July’s $50 billion loss in the high-profile Yukos arbitration, while the firm was publicly embarrassed for advice that it reportedly offered to another major client, BNP Paribas. Powerful entities routinely ask Cleary to push the envelope in international law. Lately it hasn’t worked out well.