Some emails sent to my @me acct never make it, but they make it to the acct I have setup to forward email to

I have an @me account that is use for all of my emails. I also have a "backup" account that any emails sent to my @me account are also sent to this one. Some emails are only making it to the "backup" account and not my @me.com account.

I've checked and the emails aren't in my junk file. They just don't show up but they do get forwarded (through my icloud settings) to the backup account.

What can I do to fix this? I don't want to check the backup account everyday or put that account on my phone but if need to receive these emails (all for school).

Thank you!

P.S. I'm selecting iPhone, but the emails don't show up on the iMac or if I log into icloud. They just aren't there.