Hardware and performance

So what changed two weeks ago?  And, if nothing, have you checked your RAM?

I would suggest you to monitor your system resources using nagios probes and nagios_graph. 

Often density of use increase is not addressed when setting up moodle at first time of exploitation life. 

Check also if service goes down because Apache goes away or if your Mysql server goes down... Often when a system goes out of memory, some processes are discarded to leave system core safe... i had several cases when mysql goes done before other processes, breacking anyway the service. 

Load will not so much come from amount of users, but from amount of concurrent users playing on the site, and multiplied by density of resources that are downloaded by users. 

A big moodle log table can also cause some kind of slow queries sometimes, it should be cleaned or even routed to a physical file drop down engine....

Also check what can happen with crowded courses, f.e : a course with all your users inside. Some processes used in cron could have a big work to do in such cases, moreover if people get really active....

What cache strategy are u using ? 

For something quick, suggest using terminal and viewing 'top'.  It could be, as already suggested, that the DB server on the same server is struggling to keep pace with the 'traffic'.

Also check the config of apache ...

# prefork MPM
# StartServers: number of server processes to start

? running # worker MPM?

As far as a dedicated server for DB, may not be a bad idea.  One can dedicate nearly all the memory of that DB server to nothing but DB, thus, also, allowing increasing apache servers on the web server box, etc..

Could be a combination of factors ... how Moodle being used, config of Apache and/or MySQL.   For a tool to check your DB, try mysqltuner.

No 'quick fix' without investigating the whole system.

'spirit of sharing', Ken