most hosts place a limit on the amount of server memory that is available to an application pool in shared hosting. If the application consumes more than the limit it forcibly recycles that application pool to clear the memory. If an application frequently hits that limit it causes frequent recycling of the application which impacts performance and perceived performance of the site, so you generally don't want to be hitting that limit frequently and you don't want the application to recycle frequently.

As far as I know Arvixe provides 250MB and that generally is enough to run mojoportal without problems. However if you add multiple sites it is possible to start hitting that limit.

Also many hosts let you setup multiple web sites with one hosting account (I'm not talking about mojoportal multi sites feature here I'm talking about IIS web sites) but they generally give you one application pool so resources are shared across those sites and if you add more sites it will not have enough resources for them. They make it sound like you can add more sites but you get what you pay for basically, they don't keep giving you more server resources.

If you are not satisfied with your hosting you could try another host. I've never heard a single complaint about i7MEDIA hosting for example. I suspect that hosting is a tough business and many hosts are probably struggling more and more because cloud style hosting like Azure are disrupting their business model more and more.

system log not being written to is an indication of file system permissions preventing it from writing to the log file.

it could be bad permissions on the log file itself, you could try deleting the file /Data/currentlog.config

if folder permissions are good that file should be recreated automatically, if not then folder permissions are bad.