In AVRStudio 4.13 beta: Select several lines of text, then drag the lines to a position below the original text's location. The text is inserted below the desired position by the number of lines moved.
My guess is that the lines are being removed, which changes the line count below that section, but when the lines are re-inserted the insertion position has not been adjusted for the removed lines.
If you need some screen-shots, I can provide them.
Workarounds: Either: a) Take into account the number of lines you are moving and select a position that number of lines higher, or b) use the Cut command to cut the lines, then Paste them where you want them.