There are 2 things here. The first is that the file name needs to be sorted out, using some kind of counter. Else you'll be simply overwriting the same pdf file over and over all the time.

The second issue, is that I believe there is a bug in the export inside Manipulate. This was brought up before. Here is a link

Export[] in Manipulate, infinite loop

Putting export inside Manipulate, causes infinite loop. Here is an example of how to see this problem. I made a Manipulate which exports the current plot. It uses a counter so the name can be seen clearly from the file system. You can see that, when you run this, that a new PDF file is being created, each with new name, however, this is done without moving the slider.

Here is the code
Someone from WRI should really look at this issue. If you see the same problem, I suggest to send a bug report to support@wolfram.com just in case.  Watch out when you run this code, as the file will keep on being created all the time. So need to stop the Manipulate (delete the cell) to stop the files growing (else you'll run out of disk space).

Just in case I will aslo offer another solution that I myself use often. From my point of view an ideal snipet of code that does the job conveniently with a click of a button is ( note the part {plt, ControlType -> None} localizes variable plt so it won't leak outside Manipulate ):

Any chance that the controls can be included in the export image too?