Can't possibly be too many connections on your site, when your stats look like this:
There are currently 20 users online. 2 members and 18 guests
Most users ever online was 161, 02-01-2014 at 04:16 PM.
That's completely insignificant traffic to a server.
It more likely means that the host server has too many connections, possibility that it is either a way oversold shared machine, or it is undergoing a DDoS attack on another site hosted on it. (Or both.)
I mention this for you to tell your host, when they try to blame you which they always do. It's not you.
However you can also help yourself enormously by doing some optimization work. Here's what your site looks like to IE10 browser on fast cable connection.
http://www.webpagetest.org/result/140306_GS_A1/
I've seen alot worse but not a whole lot worse.