Sickness by default is an absence type. Absence types are typically recorded by line managers or HR administrators as opposed to requested by employees.

The intention is that an employee requests holiday or maternity leave, etc.. an event that can be planned and requested, however absence is not expected and in that case the employee would inform their line manager or HR administrator which in turn would record the absence.

However if you wish to allow your employees to request Sickness leave you can still make the Sickness event types available to employees for requesting if you change the base type to be "leave".
Just go to Administration | Event Types and Allowances, select the absence type you wish to modify, click Edit and in the Event Type Details section change the Type of Event option to have a "Leave" base type - e.g. if it is Allowanced Absence you can change it to Allowanced Leave.

Submit your changes and your employees will be able to request this event type.