Not on the battlefield, at least not yet, though that has come to a stagnating, grinding crawl that won't be resolved for years if ever. No, Putin is losing the war in two critical areas, the economy and public sentiment.
When this started in 2022 Putin funded the war with Russia's sovereign wealth fund, foreseeing a quick victory. That didn't happen and he has now burned through nearly all of that funding. Last week the Duma raised taxes and increased fees across the board, hitting businesses and ordinary citizens alike, rather hard. The economy is stagnant, inflation skyrocketing despite an increasing interest rate, and decreased oil revenue. Also there is an ever increasing labor shortage which has led to a slow down in both wartime and civilian production. The lack of wartime material is showing as Russia drags out things like WWII era tanks and arms to throw into the fight.
All of this is leading to a growing discontent in the civilian sector. It also means that it is becoming increasingly difficult to recruit military recruits, the support for the war on the Russian home front is cratering, as is the support for Putin in general. Recruitment is down, as sign up bonuses have doubled(while previous sign up bonuses go unpaid to the widows and other survivors). The lack of recruitment led to throwing in of North Korean troops into the fray, but that was a one off, not to be repeated.
For now Putin and Russia are putting up a good front, but they are desperate for any save face peace deal like the one Trump is pushing. Ukraine needs to just hold on for awhile longer and they will win. Russia will collapse suddenly, unexpectedly, much like they did in Afghanistan, or better yet, when the Soviet Union died. They are not winning this war, and in fact are going to lose, badly. Ukraine and its allies just need to hold strong for a little while longer.