You'll need to do some monitoring to see if that's your issue, but I think the odds are pretty good. Especially if a reboot resolves it (for a little while).

Assuming that's the issue, to properly solve it, you either need to give your server more RAM, or reduce the amount of RAM it's using.

For an older appliance running on Amazon, the first thing I would recommend is using TKLBAM to migrate your data to a new v14.1 HVM instance of the relevant size. E.g. t1.micro to t2.micro; m1.small to t2.small, etc. The newer HVM instances sizes give much better performance per price compared to the old PV instance sizes. There is a doc page here which provides a suggested workflow and some specific considerations when migrating data.

The performance increase may be enough to get your server running more reliably? If not, then you have a few other options to explore. Each one of these should help but there's no reason why you couldn't do a number of them (or even all of them):

I think tuning WordPress (especially removing excess plugins) is a great first step. Tuning Apache and MySQL may also help. Like I said, switching to a lighter weight server like Nginx is also an option (albeit quite involved).

Having said all that, unless you have a lot of connected users, Apache forking that many workers seems pretty excessive. I wonder if someone is probing your site looking for vulnerabilities? Perhaps it's worth looking into fail2ban?

If you want to install that, here's a tutorial. It's actually for Ubuntu, but I've just had a quick glance and I would expect that to apply to Debian too. Please note I haven't tested it though so can't be 100% sure. Keep in mind that TurnKey is Debian under the hood (v13.x = Wheezy; v14.x = Jessie) so you should be able to find some docs relevant to your version if that one proves useless...

Regardless, fail2ban would probably be quite useful I'm guessing...

PS I fixed the link in my previous post. Sorry about that...

The thing with website server resources is, when you first set up the website, you have very little traffic and a minimal install footprint. As time goes on, additional content and plugins tend to be added (each adding a small amount to the resource overhead). Many WordPress plugins are poorly coded and in my experience many of them have memory leaks.

Also traffic tends to increase (both wanted traffic from the intended audience; plus unwanted traffic from hackers looking for hackable targets). Generally memory leaks are exacerbated by the number of connections. So your site may well run fine for ages until you reach a critical traffic limit where all of a sudden things start going wrong. The line between everything seeming to be fine and a crashed server may be as simple as one additional plugin, or a couple of extra concurrent logins.

Please note that a hacked server and/or WordPress malware infection is also a possibility which I haven't previously mentioned...

If a reboot is (temporarily) resolving the issue, then I'd nearly put money on your server running out of RAM (and I'm not a gambling man). As discussed above, that can be caused by misbehaving WordPress plugins and/or unanticipated (and perhaps unwanted) traffic, among many other things (including malware).

Like most somewhat technical problems (e.g. your lawnmower won't start, your car stalling or your server crashing) to properly resolve the issue you need to first understand what the problem is. So the first step is to do some diagnosis. As insufficient RAM is a fairly common cause of WordPress server crashes, monitoring the RAM usage and the remote connections are good ways to see what might be going on.

Once you have diagnosed the issue, then you can decide on the best way forward.

Thanks for posting back to share your experience with others.

First thing I noticed it was running out of RAM and found a log entry sjhowing that the mysql process was being terminated (giving me the error).

So as a quick fix I created a 1 Gb Swap file to match the existing RAM and the issue has 'gone away'.

Next thing I did was delete all unused Plugins as a just in case maneouver.  While doing that I noticed that a lot of the existing plugins are showing as 'not tested with current version'.

Just a guess but after the upgrade to 4.6.1 one (or more) of those plugs may have started to run amoke and eat up RAM.

So I am in the process of replacing the plugins with compatible replacements.

And WP has release Version 4.7 so the fun never ends lol.

Thanks to Jeremy for pointing me in right direction!

I am also having this issue.  It started happening about 2 - 3 weeks ago.  A reboot always fixes it and I was gong to set an automatic reboot say twice a week until I saw this thread.

Could this be a bad patch given that this is happening to multiple instances?

I will check the traffic suggestion in the thread.