I remember that problem, was the same when printing to a pdf, but now it remembers the last place I saved based on extension. A wonderful feature! But it’s a trick to find and I cannot remember it.
You can try going to options->File Management->"File naming rules section" and selecting the "None" radio button. This may not be an option for you based on what kind of PDM system you are using. This option causes the pdf, dxf, whatever you're saving as to have the same file name as the file you are saving/printing but with a new extension. There are other options on that page that may achieve the effect you are looking for. IIRC, the option name may have nothing to do with remembering the last place you saved a dxf.
If you cannot find a Solid Edge setting, confirm you have a file open of the type that will be affected.