flt001
Not that strange : the same happens if you place an old, inactive sim card in a mobile phone. Your phone will keep trying again and again to connect to the network, despite previous rejections. Same with a router at home, once you resigned your internet connection : machines will try again and again to connect, since the error can be due to a temporary problem in the network.
Regarding specifically the ACARS system, I suppose there's a way, thru maintenance pages, to change that, but only a certified 777 engineer will be able to confirm that.