Q: Over the weekend my @me.com email address was failing to communicate with @gmail.com email addresses.  What needs to be done to fix this?

Also having the same problem here.

It started this weekend, and two emails from different people (both using Gmail) failed to reach my iCloud inbox on time.

Similar cases have been reported on macumrors forum and apple support community.

http://forums.macrumors.com/showthread.php?t=1856290 and https://discussions.apple.com/thread/6872650

There's a big discussion about this here: Gmail emails are delayed or not sending to iCloud

--Pam

I just called Apple 30min ago and the support agent (senior advisor because I escalated)  told me I was the first person reporting this type of problem, and blame everything on Gmail. If I send emails from Gmail to any other account it will arrive within the minute, clearly to me there is something wrong between Google and Apple mail routing and/or servers.