When you draw on a PictureBox, you aren't drawing on the underlying bitmap - you are drawing over the top of the bitmap. And unless you do the drawing inside the Paint event for the PictureBox using information you stored while the user was "freehand drawing" it it will not be refreshed when the form is minimized (or indeed when a different app is placed over yours and then removed). If you draw on the picturebox in the Mouse event handlers for example, then the drawing will not be persistent - it will vanish the next time the Paint event occurs.
There are two things you can to do prevent that:
1) Draw onto the bitmap that the PictureBox is displaying. This mean getting the Graphics context for the image, drawing onto it, then releasing the context (and probably Invalidating the PictureBox to force a redraw via a Paint event.
2) Store your mouse movements in a collection, Invalidate the PictureBox, and then draw all the movements from the collection in the PictureBox Paint event handler.
The former is easier to do, but you can't undo changes the user made.
The latter is more complicated, but allows you to undo user mistakes and does not change the bitmap image at all.
Have a look at this: Creating a Simple "scratch card" Control in WinForms
] it shows a way to draw over an image in a way that doesn't touch the original image at all, but which can be persistent.