How do you know that they have started processing your application and didn't send it back again ? did they tell you that by phone ?
I sent them my application on august, 19 and they refused to tell me by phone whether they have started processing or not yet, they even refused to confirm whether they recieved it or not (but i know by the successful delivery notification by canada post).
They answered me, if your application is complete we will start processing, if not we will send it back to you with a letter explaining the missing documents. till now 2 weeks has elapsed and i haven't recieved the package back so hope that they started processing unless they have lost it like your first package.
I heard that it takes 45 days form the day they start processing the application, however, if you still unsure whether they are processing it or not and your deadline is near to the end, i suggest that you send an explanation letter immediatly to Buffalo visa office about your situation and try to prove that they have lost your first application and are not responding to confirm whether they are processing the second application or not. (that is what am going to do, if they don't send me anything before the deadline)
I mean by proof that you have sent them your application, copy of sucessful delivery notification from canada post to the saudi embassy, copy of all documents that you have sent to the saudi embassy including the money order for fedex, and the fingerprint cards that you have sent. (All of that must be accompanied by an explanation letter to show them that you have done all possible efforts to get it without results or responce form the saudi embassy ).
Am saying that because the saudi embassy is not cooperative at all, so don't expect too much from them.