Illinois law defines a "business pursuit" as a "continuous or regular activity, done for the purpose of earning a profit." State Farm Fire & Casualty Company v. Moore, 430 N.E.2d 641 (Ill. App. 1981). CMLP has identified no Illinois cases interpreting this test in the context of online publishing out of the home (or elsewhere).
As a general matter, Illinois courts deem even part-time and supplemental activities done for profit to be business pursuits. On the other hand, Illinois courts have determined that profit-making activities that are temporary or sporadic, or that result in compensation only irregularly, are not business pursuits. See for example the Moore case above.
Therefore, if you live in Illinois, you may be in danger of losing coverage for your online publishing activities if you make money from your website or blog, such as through advertisements or a tip jar, unless those activities are temporary or sporadic.
Note that specific language in a policy might lead a court to a result different from the overall state trend.