Comment 3 for bug 43730

You'll note that Inkscape differentiates two types of dialogs - temporary dialogs such as open file, save file, etc. and permanent dialogs like fill and stroke, etc.

The design is this: Dialogs that we expect users will want to continually use, such as if they wished to experiment with several fill colors in succession, or change line styles of several different lines, are kept open until the user explicitly closes them. Dialogs that are typically single-use things, such as open or save-as, are automatically closed after use.

The export dialog is sort of a grey area - for some users it is used essentially the same way that the save-as dialog is used, to quickly export a png and close. However, the design intent includes the use case of icon designers who may be exporting pngs at multiple sizes, or that will be individually exporting several items from the document. For these users, clearly the dialog should stay up.

Anyway, not to argue that one use case is more important than the other, but just to explain why it behaves this way presently. I know it's lame to say, "It's not a bug, it's a feature!" but... ;-)

We have several suggestions in the Inkscape feature request tracker for ideas on improving the export dialog, so if you'd like to influence the future design of this dialog I would encourage finding and commenting on the appropriate tickets there.