Caching Problem, Site Displays Days-Old Version

Hello, I recently came across a problem with my site that seems to be related to caching.

Site

Problem:
For the last few weeks, off and on, my front page (home) will display latest posts, but not really; it seems to stay a few days behind. Thus, my latest 3 or so posts, depending on how often I am publishing, won’t show up on my homepage section. They do exist as published, as I can type in their links manually.

Additional Info:
I guess this has to do with caching, am I right? Now, sometimes when I am logged in I don’t get this issue, but viewing from a different browser or my phone shows me this error.

I am using a combination of caching and CDNs on this site. I have MaxCDN installed for larger files, CloudFlare for scripts and whatnot, and they are all tied together with the W3TC caching plugin.

I don’t even know where to begin to debug this problem. Can anybody point me in the right direction? I did try to look up this issue in the WordPress forum, but I don’t even know the keywords or how to describe this problem, so my searches are not coming up with seemingly relevant results. Thanks in advance!

Christian E.