I have travelled to the U.S. seven times since last September. I have a British passport, ESTA, and an American spouse.
On just one of those trips I had an ESTA issue. Shortly after OLCI opened (not that you can do OLCI on these routes) I received an email from the CBP saying my ESTA had expired (not was cancelled). The CBP guy at LHR made his usual checks to allow me to fly, and also "fixed" the expired ESTA. No ramifications to my Global Entry.
On the other six trips there has been no issue.