This can be achieved by modifying the Web Forms Resource.
Administration tab-> Security and Role Management-> Role Management-> Web Forms-> Change Calendar
Then select Edit to modify the Resource.
To have the filter persist for the Change Calendar string, the Additional Where Clause must be separated from the (sched_start_date>0) that was already there. (I.E: ADDITIONAL_WHERE=(Your Clause) AND (sched_start_date>0)
The example below is filtered out by Change Order Category, but the Categories "Code" must be entered into the clause, not the category itself.
So any Change Orders that have a Category Code of 'PET' or 'PEN' will not show in the Change Calendar by default.
This can also be verified by viewing the Additional Search Arguments from the Change Calendars Search Filter.
The additional WHERE clause should automatically be entered here.