Greetings,
A lot of people are having the same issue regarding the Save As command in Actions. However, the solution is simple and it requires no scripting.
Try this: Create a folder (eg. temp) in a removable media (usb flash drive) and use this folder (temp) when you record the "Save As" action. When you're done recording, eject that media.
The next time you play your action, Photoshop will take you to the same location as your opened file, since it cannot locate the previous destination (temp). It will however ask for a filename (identical to the opened one) so you can click OK, or hit Enter. Quite useful when you want to eg. save your opened raw files to JPG in the same folder.
Please notice that it is important that you DO create a folder in the removable media. If you go ahead without a folder, Photoshop (when you eject the media) will save to a hidden folder in System called Volumes (Mac OS), which is hidden by default.
I've tried it on a Mac, but I'm sure it works the same on Windows as well.
Hope this helped. Just remember NOT to insert that media when you playback your action in the future. Rename the media if necessary.