After uploading file into Azure blob storage I could see original file time stamp is lost.
Some how I need to preserve original file time stamp. Azure blob storage doesn't allow to programmatically update "Last Modified Date".
Please share if any one has come across this situation before.
Since Last Modified Date is a system defined property, you can't really preserve it. Any time a blob is updated, this value will change. One thing you could do is keep the original date/time when the blob was created as blob metadata entry if you're interested in finding out when a blob was created. This however is not fool proof as if the blob is re-uploaded, this value would either change or removed.
Another thing you could do is keep this information in a separate place (Table Storage for example).