A number of military commanders fell out of Churchill's graces during the war. In hindsight, a lot of them may be seen as being vindicated by history. A couple that lost their jobs due to pressure from Churchill and/or complaining "too much" were: Archibald Wavell - replaced first as Commander of British forces in the Middle East, and then replaced again as Commander-in-Chief of American-British-Dutch-Australian Command after the fall of Singapore. In both cases, he successors faired no better, begging the question of the judgement of Churchill's decisions http://en.wikipedia.org/wiki/Archibald_Wavell,_1st_Earl_Wavell Claude Auchinleck - having replaced Wavell, it was Auchinleck's unenviable duty to carry out Churchill's orders without receiving the required material support. He was in turn replaced by Alexander after he could not carry out Churchill's wishes. http://en.wikipedia.org/wiki/Claude_Auchinleck Air Chief Marshal Longmore - as AOC in C, Air HQ Middle East/Middle East Command, Longmore had the unenviable duty of not only covering the ME, but after sending aircraft to Greece (which was supported by Churchill, who promised reinforcements and resupplies), did not receive the replacements promised. Ordered back to London by Churchill to discuss the situation, he was then sacked by him for complaining too much. http://www.rafweb.org/Biographies/Longmore.htm
There Is also Stuffy Dowding and Sir keith park, who both fell foul of Churchill despite their victories in the Battle of Britian http://en.wikipedia.org/wiki/Hugh_Dowding,_1st_Baron_Dowding http://en.wikipedia.org/wiki/Keith_Park
General Sir Alan Gordon Cunningham - another one who fell victim during the North African campaign http://en.wikipedia.org/wiki/Alan_Cunningham
Thank goodness he didn't sack his CIGS General Sir Alan Brooke. Brooke was prepared to risk head-to-head table-thumping rows with Churchill, according to his diaries, and prevented several of Churchill's more hare-brained schemes from taking place.