Not sure if your server is different in some way but as far as I know all sub domains are really nothing more than a link of a different name pointing to the resources on your main domain
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For example lets say you have a directory called images and your website is called myweb.com you could access the images by typing myweb.com/images.
images.mysite.com would simply be pointing to myweb.com/images.
All of the content is still on the same server in the same account. If something is messing with the subdomain it most likely will mess with main domain.
Subdomains are really for organizing different types of content for different users. In this example I have a website in the rv industry with a subdomain. Once a year we do a classic car cruise-in. The people interested in the cruise-in may or may not be interested in the main site thus having the two different but related sites on the same server. For the cruise-in the subdomain is advertised making things simpler for visitors to get where they want to go.
Now if the server has issues it effects both main and sub.
If you really want to seperate the images maybe a second account with the same host using a different domain name or better yet a high speed content delivery network (cdn). I use one for a couple of videos. Just look up cdn in your preferred search engine. Also check with your host, some have been known to have a white list for hot linking meaning you could turn on hotlink blocking yet create a white list of sites allowed to hotlink.
Hope some of this long reply helps.