No you cannot as of January 4, 2011. It is now changing due to the company going under. Sears Holding Corporation is in fact over debt due to the economy. Ie: Individuals not paying on their cards, and the stores are closing due to a lack of consumers. The gas stations that once accepted no longer do, therefore this is not an option as a sears card holder anymore. Your best bet is to apply for a gas card at the many stations available to you.
Does your SEARS card have a VISA logo. If so then you can buy gas with that card at thousands of locations nationwide