Going strictly by the calendar, it is not TOO surprising to hear that the Ronde was run without interruption during the war.
In 1939, no war when Ronde was run in April.
In 1940, same thing, Germany didn't invade the Low Countries until May 10th.
1942, 1943 and 1944, Belgium and northern France were occupied by Germany, but there weren't any land battles going on. I haven't heard of any targets for bombers being on the course either.
D-Day 1944, well, that was June, after the Ronde. By November the Allies had already cleared Belgium and France where the race takes place. April 1945, the war was almost over, certainly it had passed by the race course. I guess the locals asked the US/Brit military for permission to run the race and they got the go-ahead.
LBL, that I am surprised about. As ingsve says, the Battle of Bulge took place just 3 1/2 months before the race, and there was huge aounts of fighting all over the race course. Bastogne, Stavelot, Houffalize, and other towns all suffered shelling and in some case, house to house street fighting. Some of the roads were reduced to dirt, going by pictures I've seen of the battlefields.