posts appear to be there but they're not

Unless you provide a link to a page demonstrating the problem, no one will be able to offer much in the way of assistance.

My site is https://bobcavanaugh.pcriot.com and it is happening on every page that is clicked on.

Try resetting your custom permalinks back to the default setting. If this works, then try asking your hosts if mod_rewrite is running on your server.

What exactly is mod_rewrite?

It’s the Apache (server) module that handles the rewriting of urls from Url A to Url B. WP uses it to create “pretty” custom permalinks out of ugly, default permalinks.

Ok I reset the permalinks and now it’s working again. However, while we’re on the topic of permalinks, my ideal structure would be something like this, yourdomain.com/April2011/06/postname. Is there a way I can set it up to do this?

Not quite like that but close. Have a look at Using_Permalinks for a list of the permalink structure tags you can use.