This is because by nature a screenshot is a bitmapped (indexed color) image without aliasing. That is, the letters are solid colors with no aliasing to smooth the transition to background.
When you resize the image, a process called interpolation takes place. basically if the lower-case "L" is 3 pixels wide in the original and you size it down by 50%, this means that logically the width of the stroke is now 1.5 pixels, which is really impossible. So the program interpolates the values to whole pixels, making some on the edge 50% of the original color value and only one pixel 100% of the original color value, creating a visual "emulation" of the original at 50%. The result is usually a blurring of all sharp objects, such as type.
If you stay with indexed color, chances are good many of your characters will disappear in the interpolation, so you need to convert it to RGB and save as a jpg, not a gif. A gif or other indexed color format will only work IF you do not size down the screen shot.
Screen shots are a bear if you want to size them down. Sometimes you can retain most of the info by using an sharpening technique, and if you absolutely want to retain legibility you can type over the old text.