Your site is slow enough to be virtually unusable for me .
It took approximately 40 seconds for the first page to load, almost 20 seconds to load a couple of the other pages, and approximately 16 seconds to “refresh” the page displaying the plugins in use on your WordPress site.
And therein, lies a clue - what is it, 40 plugins installed? (I admit I got confused counting as the screen scrolled).
You can easily over-burden a shared server by operating plugins on a word press site - by operating too many plugins and/or having inefficient plugins.
Log into the shell and check your server load - if you are running a number over 20, that may be part of the issue (though it might be your site that is causing the load, with very few hits to your site that may not be the case.)
Temporarily disable as many plugins as you can possibly do without, test your site and see if there is a change.
If the site runs better without the plugins (and it is almost guaranteed that it will) consider whether you really need these plugins and, if so, then start to add them back on one at a time until you see the performance again begin to suffer.
By experimenting this way, you should be able to see which plugin is problematic , what combinations of plugins run well together, and which ones are just too much for your server.
Relying on akismet for comment spam prevention can be hard on a server - if you have sufficient spam being caught, consider that all that spam-tracking takes processing time and hurts your server performance. You can mitigate this somewhat by only allowing comments where you really want them, and disabling them if not important.
After you site has run awhile, you may need to index your database tables to keep performance “sharp”. There are many helps on doing this that you can locate via Google.
Note that the plugin usage may well account for the slow degradation of your site’s performance. Most people add plugins as they discover them and decide that they might be useful. When your site is new it usually does not have too many plugins installed, but as your site matures and you find a “new thing” adding plugins can get out of hand.
Of course, you can also contact support, but I strongly recommend you research these areas first… you might be able to solve most of your problem(s) yourself!