You can't. If your image is 200x200, then that is how many pixels of information it contains. If you scale it up, it's still the same amount of information only you have to spread it over a wider area.
Think of it like this - say you have an image that is one pixel and that pixel is blue. Now you want to scale that image up to two pixels. What color should the second pixel be? Answer: it can be anything. There is no information in the first pixel that can authoritatively decide what the second pixel should look like, there is no information available.
So, it's not a matter of "loosing pixels" as you put it, it's a matter of adding new pixels with no information on what they should look like. So the resizing uses the information it has, which basically says "make inserted/new pixels same color as closest adjacent pre-existing pixel".
There are algorithms and techniques for interpolation (guessing) what the inserted pixels should look like to avoid jagged edges and such. Wikipedia has some good info on various interpolation-based scaling techniques and supersampling as a starting point. Note though none of these techniques create new information, they only smooth out edges and make the scaled image look less jagged.