Are you using digital (certificate-based) signature? If so then are you signing in a browser? With the browser you may not know the real location where the PDF resides. If this happens on the desktop the change the name of the signed PDF in the Save As dialog and pay attention to where it saves it, Then check if the file is there. It should be.
If you're using electronic signature then someone else should chime in.
Are you using digital (certificate-based) signature or electronic signature? Does the 'Save as' dialog come up in the process of signing or do you invoke it explicitly? Which product (Acrobat/Reader), which version (including minor) on which platform (Mac/Windows) and which OS/Version are you using? If you save the file to the desktop, can you find it there? Is this just USB problem? Can you copy a file (any file) from the desktop to your USB stick and find it there?
Please, provide as many details of your workflow as you can. I save my digitally signed PDFs to USB flash drives all the time and never saw this problem.