Sometimes Photoshop files in Unity don't like to acknowledge the alpha channel unless there's an actual background layer. Try flattening the image.

I should add that Photoshop files support plain ol' transparency, as well as transparency by using an alpha channel. Most of the time you'd want to use an alpha channel, since regular transparency tends to result in white fringes because of not being able to specify a matte color.

Make a new layer behind everything and fill it with a solid color. If any pixels are at all transparent, unity will use the resulting image transparency and ignore the alpha. This is non obvious sometimes when some pixels are slightly translucent, or maybe a few pixels in the corner end up being transparent.

Been wrestling with the seemingly randomness of this for a while...

The only thing that works for me when this starts happening is to take a texture that is working, say a Unity default Grass texture, and replace it's contents with yours and save with a new name.

That's because Photoshop will sometimes choke on transparency, and .jpg files, being exported from PS, don't support transparency at all. Transparency in png. files, however, is much more stable. You can export png. files from Fireworks, Paint, and Gimp.