A few days ago, I reported this problem on ticket #0022389, for a different PC. I am now experiencing this problem on a second machine and this time I can not get un-stuck form the update loop.
Per your feedback on ticket #0022389, I have contacted Battleeye support, directly. I wanted to alert you that Battleeye is still being a pain in the ass, so I will paste the text of my e-mail to them, below.