Two likely causes:

1. You're not reducing by an integer multiple (ie, 1/2, 1/3, 1/4). When you do that it's easy to "collapse" the pixels (like with a 1/3 reduction every 3 pixels becomes 1). When you picket a non-integer reduction some applications produce poor quality results with jagged artifacts.

2. When you go to save your JPEG quality is set too low. You're getting JPEGs off the camera but the quality is generally set to 1.0 (on a scale of 0 to 1) while when you go to save the default is usually around 0.7 (or 70 if your application talks about a 0 to 100 scale). Increasing the quality...well, increases the quality but at the expense of increasing file size.