Do you have another variable or function with the same name? I mean public String sendingSign {get; set;} or maybe public String getSendingSign()? These would "shadow" your action function. Do you have more than 1 controller extension in <apex:page> tag? they'd be checked for matching function names from right to left (so if you have few classes maybe it's calling the match from a class you're not looking at)
Open up your browser's JS console/network panel, see if there's any traffic recorded at all when you click the button...