When I tried my first correspondence match things did not work in what I would think would be a reasonable way.  I would think that I could make a move, go away, and get an email when my opponent makes a move.  

My alerts settings has this box checked: ONLINE CHESS: my move, low on time, game challenge, etc.

However, I have only ever received an alert from chess.com when I have been low on time.  I lost my first match because I ran low on time at 2AM and didn't check my email until after 10AM!

I have checked my spam filter folders, and messages from chess.com are not being filtered out.  What's going on here?

Login more often to check the status of your games to that you don't lose out

Sure, thanks for the tip.  How about if my cell phone doesn't ring all of the time I'll just be sure to check for missed calls every few hours?

Not to practice thread necromancy, but I've got the same problem, and I can't fix it just by checking in more often, as the site is blocked where I work for what should be obvious reasons.  If I get a low-on-time notification at 4 in the morning and don't see it until I'm at work, unless I can get to a laptop that can reach a working wifi connection before noon, I'm out of luck.  It's nearly happened to me twice already, but I've been fortunate enough to find a way around it.  It won't always be that way, and through no fault of my own.