Suzuki Swift 2013: Blown transmission

I bought my Suzuki Swift Sport in 2013 and have a three-year/100,000km warranty. I cover a lot of kays a week and spend about an hour a day in stop-and-go city traffic. In hot weather, when I put my foot down there would be no acceleration — I would have to pull over and pump the pedal for about 15 seconds before it would go again. The dealership said no problem was found after taking it for a drive around the block. In winter, I had no problem. Then, driving home, there was a loud bang and all of my warning lights came on. I got Suzuki to tow the car in and, after running diagnostics for the last week, they have found that the transmission has given up. Since I am at 94,000km and still in the three years I thought the warranty would cover it. But they are claiming that since I missed the 50,000km service, even though I've had the major 80,000km service, it will void my warranty.