What impact did wartime failures have on Russia?
In my mind, the cost and toll of World War I helped to drive home the point to Russian citizens that the government needed to change. The anti- Government forces had done an excellent job of disseminating the message that the Czar was an out of touch autocrat who needed to be reigned in and completely overrun. The fact that Russia endured some of the highest death and casualty count in the war, and that there was never a clear mandate from the citizens that would validate Russian presence in the war also helped to underscore the fact that the Czar was out of touch. Instances like Bloody Sunday, where the Czar's men were perceived to have shot at a crowd of protesters, some being women and children who wanted decent wages and food, helped to paint this picture. In the end, this is what helps to bring the Czar down, and the failures in war ended up being the final straw which causes the Russian people to rebel.
I'm assuming you mean failures during World War I. Russian troops were poorly prepared and had limited supplies or adequate clothing for most of the war on the eastern front. This led to a large number of casualties (3.3 million), battlefield losses that surrendered large amounts of territory to German troops, and it ultimately led to the Russian Revolution in 1917.
The Czars, unable to fight both the Germans and the uprising at home, made a quick peace with Germany at Brest-Litovsk, ceding the Ukraine and more to the German empire. The population turned against the Romanov dynasty and imperial Russia became Soviet Russia by 1924.
The main impact that the wartime failures (especially the loss of people and land) had on Russia was that they led to the end of the Russian empire and they led to the rise of communism and the Soviet Union.
Up until WWI, Russia had been ruled the Tsars -- in other words, it was a monarchy. But the failures of the war, among other things, made people pretty unhappy with the way their country was going. In 1917, rebellions broke out that eventually led to the Tsar's government being overthrown.