It seems as if when downloading the show from an iPhone I have artwork for the mp3 file. If I download the show from iTunes from the usual que then sync them to my iPhone to listen to while at work, in the car, in bed, while walking or in the bathroom, I have no artwork on my computer or transfered to my iPhone. The same think happens with my iPod... no artwork.
The only way to get around this is to add my own. There are only a few podcasts that I save after listening, FTL is one. I get a good graphic and paste it into the artwork filed just like I would with a music file. It makes the podcasts look much nicer in iTunes and easier to find on the fly on the phone.
It seems to be hit or miss with respect to getting artwork to download with podcasts from iTunes. I don't think it's specific to FTL.
I use a Mac.