I use my ISP mailbox or another paid one for "important" mail to make sure I have someone to call if I have a problem. I don't think the great big free ones can be that reliable all the time.
Have you tried sending yourself mail to your other mailboxes to see if you can duplicate/confirm not getting the mail? Is it everyone you send to or just a few? It's hard these days to figure out some problems what with firewalls and other protection systems (especially people at work at companies with sophisticated computer systems); not every business likes the free accounts since they're so susceptible to spam, they automatically block them.
I have an inexpensive dial-up account (even though I don't use dial-up) just for the other features (e-mail, free web site without ads, etc.). There's a wonderful/easy ISP,
http://www.isp.com that's less than $10 a month that I got for a friend and we've used (she doesn't have credit cards so I pay with mine and she pays me back) that for a couple years. Even though I have Comcast cable to get online, my own dial-up is
http://www.arczip.com and I've used them 6-8 years and highly recommend them. I always keep a dialup around so I can get online during vacation or if something happens to cable, etc.