I have never seen where lines get lost when I paste them. However, when you use visual mode (shift-v), usually you only need the first "y" to yank lines. It's likely that when you press the second "y" and move down, you are actually yanking the top two lines (which is what is supposed to happen). You probably just need to stop pressing "y" twice. (Hint: press "y" once in visual mode, or twice when you want to yank the current line in normal mode).
You can yank multiple lines in a variety of other ways. For example, 14yy will yank 14 lines. If you use gvim, you can use the mouse cursor to select text. You can also do y14j to yank the next fourteen lines, since y, followed by a movement command, copies everything in that movement command.