Although wars in CoW usually get decided by a battle or in a day or two, there will always be some games that just drags on and on, with both sides suffering heavy casualties while making little gains. My current 1.0 game as Libya is an example of this. On day one, I prepared as I usually would against Algeria and Egypt, stacking troops at their respective borders. However, on day two, an unexpected Italian invasion took over the cities of Tripoli, Sirte, and Benghazi, with only Sirte being still a functioning IC when I recaptured all three cities shortly after. Because of a built IC in Sabha, I was able to retain some of my troop production capabilities as well as rebuild the IC in Tripoli.
I began to build a submarine force to protect my coasts, but before it can be completed, Italy again attacked, this time at Ras Lanuf before swinging west to Sirte. With the second capture of Sirte, the city was now completely destroyed, leaving me with 4 provinces able to produce troops. In the news, I could see Italy has both a larger army and economy, and I expected to lose eventually.
Yet, miraculously, this war from day 2 dragged onwards, until now, at day 14, we're both still somewhat in a stalemate. I managed to snatch Tunisia and the island of Malta from France which had been defeated by the UK and Germany a day before, helping my economy a little bit. With a complete sub wall, Italy had much more difficulty attempting to board my coasts. Although he has a decently strong destroyer force to counter my subs, note this is in 1.0, so I can simply avoid those destroyers. During this time period, he also made several mistakes, most significant of which was the lack of research in interceptors. Although his tacs are at level 3, his interceptors remained at level 1, while I had leveled my own interceptors to level 4 with my limited economy as well as researching SPAA. I launched suicidal raids with AT on Sicily and Cagliari. Although each time I staged these small counterattacks, the troops would most definitely die, the capture of the food provinces dealt significant blows to the Italian economy.
Now, as day 14 comes to a close, I have gathered almost my entire land army, a measly force of 14 units, to attack Italy proper with some air cover. Hopefully this counterattack will deal a fatal blow to Italy, if not conquer it completely. I have never had such a long stalemate, and I'm quite happy for this fun war.
Day 2 Europe and Africa: when the war began and I lost Tripoli (capital), Gharyan, and Benghazi early on.
Day 14: much has changed around us, yet the stalemate remains. Tripoli endured a rocket attack, while my capital is now at Al Jawf, the southeasternmost province in my nation, furthest from Italy. Italy now has 7 production centers, while I have 4. It is simply a miracle that I was able to hold out for so long. However, I must try to end it now, or I will truly lose.

Likely the war with the most casualties so far in this map, but it may change. North of us, UK and Germany are preparing to face Caucasus and Russian Empire. From the news, I would judge them to be of inferior skill to Italy or me (definite bias here), but Caucasus does have the largest army, so I would expect a deadly war.
Now, I ask: what was the longest stalemate you had?
"As long as there are sovereign nations possessing great power, war is inevitable." Albert Einstein
"Giving up is not an option in war, for it proves one's incapability and incompetence as a leader." - Me (Little Racoon)