Generally hosting like Arvixe is budget shared hosting and while they may let you add more and more sites I don't think they don't keep giving you more server resources such as memory and processing for each site. So doing that is ultimately going to slow down all the sites. As you may know there is usually a slow startup for an asp.net site on its first request because asp.net has to do a bunch of JIT (just in time) compilation of files, but after a few requests that stuff is done and it should be fast. But usually hosts have a memory limit on the web application pool and when this is reached the application pool is recycled and that means all that stuff has to be JIT compiled again. If you add more and more sites all using the same allocation of memory it will starve them and they will keep recycling because they keep reaching the memory limit right away and this kills performance. Unless you are paying for higher quality hosting usually they only give you enough memory for one IIS web site even though they will let you create more sites. You get what you pay for.
So instead of creating sub domains which are separate physical installations that require separate memory and server resources, it would be better use of resources to have only one physical installation with multiple sites by host name all running from the same single installation and a single IIS web site.
This would require a dedicated ip address that is not shared by other customers at your host, such that the first site would be accessible by ip address. Then you would only need to add dns settings for the additional host names all pointing to the same ip.
"I have tried to add a host name entry at new.site.com but this gives me an error."
you should start a new thread specifically about that problem and post the error detail from the log.