I just ran into this problem. I'm working with 16-bit colour maps that contain 65,536 distinct colours. My original BMP shows a DPI of 95.99 when opened in Paint.NET. I then save it as PNG, and when I open it again, Paint.NET shows 95.96. So far so good, the image still works for my purpose.
However, I ran into trouble editing the PNG and saving it again as then the DPI drops further to 95.94. I didn't know that was happening, so didn't realise that when I loaded the image with Microsoft's System.Drawing namespace, the image was getting slightly resized and smoothed a bit, giving me only 45,874 distinct colours in the colour map.
So there's definitely a chance for something to be lost here if people aren't aware that this happens and don't realise they may need to compensate for it when using other applications. I think Paint.NET needs to apply a small adjustment to offset the drift.