Account suspensions are used by the Abuse team as a last resort. In most cases, the Abuse team only suspends journals when we cannot work with the user to resolve a violation of the Terms of Service. (Immediate suspensions are done for certain reasons, including but not limited to Denial of Service attacks, account breakins, and journals created solely to abuse.)
If your journal has been suspended, you should check your e-mail to see if you've received a warning or an explanation. If you haven't, or if you have any questions, visit http://www.insanejournal.com/support/submit.bml to open a request under the "Abuse" category or send an e-mail to firstname.lastname@example.org from the validated e-mail address of your InsaneJournal account. Be sure to include your username. The Abuse team will respond as quickly as possible, though in some cases it may be several days. Please do not open up multiple requests, as this will only serve to delay the process.
In some cases, suspended journals will not be reinstated. These cases include but are not limited to journals created solely for abuse, journals belonging to users with an extensive history of abuse, journals created to circumvent directives of the Abuse team, and journals belonging to users under the age of 13 (see http://www.insanejournal.com/legal/coppa.bml for more details on the Children's Online Privacy Protection Act).