In your custom filter Section you can include a Section where the Page Context is sourced to "Data Page". That Data Page can invoke a query using an Activity that does an Obj-Browse. You now have a Data Page named, for example, "D_CustomerFilter", with a Property such as ".StartDate", the value for that Property having been previously persisted and now retrieved.

You now need to transfer that Data Page's ".StartDate" value to your Report Definition's Custom Filter Section.

Name the custom filter prefix "CustomFilter". Prior to the filter Section being launched in a modal window, a page named “CustomFilter” will have been created for use as its page context.

Following the Obj-Browse In your "D_CustomerFilter" Data Page's load Activity do:

   Property-Set  CustomFilter
        .StartDate =  D_CustomFilter.StartDate

The only thing you are still lacking is a way to persist the last-used ".StartDate" value.

You can define an "On-Change" action that persists the most recently set value. Only someone with a certain Access Role would be allowed to do this.