If an SSO (Short Sale Offer Addendum) was included at some point with your offer and the September deadline of the 24th was included, should that date come and go with no approval from the seller's bank, you are no longer obligated to that offer. If you choose to want to stay involved with this offer & property, you may do so by formally extending that deadline or just sitting back and letting the clock tick. If you don't formally extend the deadline, you still have an accepted offer, but are free to pursue other homes. I would suggest you formally dissolve the offer prior to writing an offer on another home should you find something you like better.
As for whether that's an impossible deadline, every transaction is different. A shorter deadline like the one you have, might be a good thing in that it may make the bank take notice and move things along. You can always extend that deadline if you choose. If the listing agent proves that the seller's lender has been making progress with the transaction and their decision, you may want to stay involved with this offer. Sometimes during this time period the seller's bank is reevaluating the current value of the home, the seller's financial situation or other liens they may have to pay out from the proceeds. The waiting period can be very unnerving for some agents and buyers because there is often a lack of information or the appearance of progress.
As for changing the closing date, that can be done as long as all parties to the transaction agree. Usually, if the seller's bank agrees to your offer, but the dates & deadlines of the offer are now unreasonable to accomplish a closing in the original time frame, the bank understands that for you to get your lending & inspections completed, you'll need more time. In most cases these deadlines are renegotiated if & when the bank approves your offer.
Short sales are not for everyone. They take a patient, flexible buyer that doesn't need to be in that home in any specific time. The process has become better than it was a few years ago, but it still can be very time consuming & stressful for all parties involved. Good luck with your offer.