You have to understand the cause of the slowdown. It’s not always a server problem.
In my experience, I this kind of situations, problem resided on theme code.
First, use tools.pingdom.com/fpt/ to understand if there is a SPOF. Then remove it.
If you can0t find it, then try to debug theme code printing time (such as timer.start and timer.stop) in more points, so you can understand what is really slowing down your site speed.