First, you can put more than 1 instance of the news module on a page, but you have to understand there are issues with doing so.  The issues have to do with caching and using AJAX, which is default.  The error message you are getting is not a lot of help in understanding the cause, but read the 'Post Your Broken Links Here' post at the top of the News forum page. You'll get a good overview of what other's found and I've provided some info there and on my blog.

What follows is my personal experience and preferences...

The issues with using more than 1 news module on a page have to do with rendering times.  Each news module will 'fetch the news' depending on your module settings.  When using the AJAX option, which is the default, I've had to refresh the page once for each instance to get the feeds to actaully show up.  The newest version helped aleivate some of this behaviour but not all.  So, my next approach was to change the settings on each instance to disable the Ajax mode. This setup works best for me.

Now, in practice, I don't like to use more than 1 instance of the module on a page due to some of the issues reported with feeds failing.  This is not entirely a News module issue, as many feed providers change their format over time, and the validity of their format can be compromised.  Due to the design of the DNN News module, all of the incoming feeds must be converted to a simple RSSv2.0 format in order to allow multiple feeds to render in a single instance of the module.  If you have one of the feeds fail, you get the download error, which should only display when in the Admin/Host account, users should see whatever feeds can be rendered and not the error.  I find that this type of usage is not something I desire or need.  In fact, the module I use for feed aggregation is the DNN Feed Browser, which gives me much better look and feel.  That's my preference.  I use the news module for single news feeds rendering, only.

Another issue, is the cache settings for the module, and more importantly the site's host setup for Caching.  These settings are supposed to allow the feeds to cache for a certain period of time, and then refresh base on those settings.  However, in practice, the caching does not function as a real timer, as you would need to setup a way to 'hit' your site in a timed interval.  This means that the caching only seems to function when users access your page.  Thus rendering is not always up to speed.  The more instances of a news module on a page makes the time to render a page longer.  That in my opinion is the single reason why I would not use more than one instance - for the most part, users tend to avoid pages, and site's that have long rendering times. 

Those are some of the issues I've encountered.