There is no information on a timeframe regarding the retry periods. You can use that button as long as you want, but if there is no Internet connection, then it will be pointless, as Internet is something that you must have enabled on your device in order to enjoy Snapchat. When there is no Internet connection, Snapchat will give you a message saying: "Failed to send". If an Internet connection is activated, then the button will change in Tap to retry.
