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Short answer
The answer to this is very much complicated by the existence of a large number of forgeries dating from the 1930s onwards. There doesn't seem to be any definite evidence that Hitler continued painting after the early 1930s, and even this date is suspect. However, although the bulk of his paintings were done before WWI, Hitler did continue to sketch and draw when leader, mostly (and maybe exclusively) when expressing architectural ideas.
Details
The latest painting by Hitler I have found dates from 1931 of a woman's head, but this may be among the disputed works regarding its authenticity. This was auctioned in September 2010 by Mullocks Auctioneers, one of several auctions they have conducted of 'Hitler' paintings. Mullocks experts
have always said they were uncertain over whether Hitler painted the pictures in pre-auction notes.
An article in the Economic Times notes the uncertainty concerning the authenticity of another 1931 (or later) painting:
The unsigned painting, which is oil on canvas, shows the grave of Hitler's half-niece, Geli Raubel. The Nazi leader was romantically involved with Raubel, who committed suicide in 1931 with his pistol. The painting is thought to have been produced by Hitler.
If authentic, this could be no earlier than 1931 as Raubel died in September of that year.
Another possible, but uncertain, candidate is a self-portrait in oil (rare for Hitler) from 1925. This claim of authenticity was made by the historian Werner Maser, the same Werner Maser who "was the first historian to claim that the Hitler Diaries were forgeries" (the same diaries which deceived Hugh Trevor-Roper).
However, claims that many paintings attributed to Hitler are fakes have to complicated things and have to be taken seriously. Hitler, an artist of little skill, is easy to forge. One early such forger was Reinhold Hanisch, an early acquaintance of Hitler during his time as a struggling artist in Vienna. Exploiting Hitler's fame in the 1930s, Hanisch was imprisoned for producing Hitler forgeries. Many of these forgeries were subsequently tracked down and destroyed on the orders of Hitler himself, but how many slipped through the net is unknown. There have also been later forgers according to journalists Jaap van den Born & Bart FM Droog.
It seems unlikely that Hitler produced any paintings after he came to power for the following reasons:
He had a country, and later a war, to run. What 'free' time he had was mainly spent watching movies and reading (among other things, but no mention anywhere of painting). Considering that a fair amount has been written about Hitler's early 'career' as an artist, it would be strange if, when talking about Hitler's pastimes, painting would simply not be mentioned.
Albert Speer, in his diaries, makes several references to Hitler making sketches related to plans for buildings etc from the mid 1920s until at least the mid 1930s, but he never mentions Hitler painting while FΓΌhrer. This excerpt from Speer's diaries strongly indicates that he did no more than sketch and draw:
All his watercolors from the same time have this quality, and even the watercolors done while he was an orderly in the First World War lack distinctiveness. The transformation in Hitler's personality, the growth of self-assurance, came later. It is evident in the two pen sketches for the great hall in Berlin and for the triumphal arch, which he drew about 1925. Ten years later he would often sketch with a vigorous hand, using red and blue pencil, sometimes going over and over his drawing until he had forced his way through to the conception he had dimly in mind. Nevertheless he still thought well enough of the modest watercolors of his youth to give them away occasionally as a special distinction.
In August 1939 (just before the outbreak of war), Hitler told Neville Henderson, the British Ambassador,
I am an artist and not a politician. Once the Polish question is settled, I want to end my life as an artist.
Whether this can be seen as a genuine desire is doubtful. More likely, Hitler was trying to give the (misleading) impression that he would soon have plenty time for painting, not war.
Admittedly, the points made here are not conclusive, and lack of evidence (of painting) is not evidence in itself. On the other hand, there can be little doubt that Hitler still sketched and drew after he came to power.
Other sources:
H. Murray, 'Analysis of the Personality of Adolf Hitler' (OSS, October 1943)
Enzo Colotti & Riccardo Mariani, 'The Water Colours of Hitler'
Martyn Housden, 'Hitler: Study of a Revolutionary'
Eugene Davidson, 'The Making of Adolf Hitler'
Albert Speer, 'Inside the Third Reich'