How to tell: If this is the problem, merely reading this will already have made you realize it, probably, but to explain in any case: sometimes the flickering line that outlines the selection is annoying because it makes it hard to see important details of the image, so GIMP gives you the option of hiding the selection, by unchecking Show Selection in the View menu. It is easy to forget that you have done this, though.

How to fix: If this hasn't rung any bells, it isn't the problem, and if it has, you probably know how to fix it, because it doesn't happen unless you explicitly tell it to; but anyway: just go to the View menu for the image and, if Show Selection is unchecked, click on it.