As you've noticed, the site seems to be in-accessible every few days, and this seems to be increasing in frequency. Today alone it was down 2 times!
In the last update, I moved the site to a cheap server, and one of the reasons it was cheap was because they really provide no support at all. Well, turns out that was a bad plan. They are not helping figure out what is causing the sites to go down.
So, I contacted some people I know and managed to get recommended to another hosting company. This one costs more, but they have a full service package which includes support and troubleshooting for issues just like this.
I'm in talks with them, and will let you know when the move is planned for - although the site already goes down so much you might not even notice