Like all attempts to preserve the peace, balance of power is not perfect.  The most obvious example of the failure of a balance of power system is WWI.

In the build up to WWI, Europe was a multipolar place.  The various countries were supposed to engage in making alliances to ensure that no one country could become strong enough to start a war.  But this did not work in WWI.  The prospect of fighting a British-French-Russian alliance did not prevent Germany and Austria-Hungary from going to war with Serbia.  Neither did the prospect of fighting the Central Powers deter Russia from siding with Serbia.

Balance of power politics helped to keep Europe relatively free of war after the Napoleonic Wars ended.  But it could not prevent WWI from taking place.