Numerous complaints in Apple’s discussion forums have spotlighted a problem preventing iCloud.com and me.com email addresses from receiving Google Gmail messages, with delays lasting hours or days.
451 4.5.3 Too many rejections; try again later.
According to the discussion forum threats, Apple’s servers have been rejecting Gmail messages since last week, and Apple engineers are continuing to work on a fix for the problem:
They are very aware of the issue and working on fixing it. They said that everyone who is having this issue should call and report this. They’ll ask you for some info that will help them. They [sic] tech said specifically that the more people that call, the easier it will be to get a fix.
If you’ve been waiting on important Gmail messages and haven’t received them, this is most likely the reason. Apple’s telephone number for reporting iCloud mail issues is 800-275-2273.