Whenever I use the Blur Tool (one of the options on the Fill & Stroke Menu) it shows up fine on Inkscape as an SVG, but whenever I export as a PNG (or whatever file type I choose) the blur either goes completely solid (hard-edged) or it completely disappears. I have made sure it is selected when I export, and it has happened every time I try to export.
I'm just wondering what's up with this...

btw I believe I'm using version .45

Try upgrading to 0.46 and see if that helps. Blur should work fine in 0.45, however. Is it just the one file that is having a problem, or all SVG files you create?

There isn't anything necessarily wrong with the PNG itself. Did you also try different viewers (e.g. just dragging it into Firefox)?