I had an Adata 1 GB SD card go bad in my Kindle. So it is possible. A couple of days after I got the Kindle I went to use it and it was dead. Wouldn't charge, wouldn't reset, etc. After talking to Amazon support and some head scratching I removed the SD card and tried it in my Palm (didn't want to try it it in a card reader on my PC because my PC is way more expensive than my Palm.) The SD card made my Palm go into a soft reset cycle, where the Palm would soft reset, show the time screen and then soft rest again. I quickly turned off my Palm and removed the offending card.
The Kindle was still dead and I was waiting on a call from Amazon customer support. FF to the next day, I get up and my Kindle was working fine! It's been fine ever since. I purchased a Toshiba 1GB SD card and it's been in my Kindle with no problems.
Definitely, check out your SD card in another device to be sure it can be reliably read.