sorry, I still don't understand it.
I retested this here with:
planner1.Display.DisplayEnd := 54;
with planner1.CreateItem do
begin
itemstarttime := encodetime(19,0,0,0) + encodedate(2013,2,19);
itemendtime := encodetime(0,0,0,0) + encodedate(2013,2,20);
end;
and it shows the item from 19h00 to 0h00. Technically, midnight today (Feb 19) is 0h00 Feb 20, day lapse is at 0h00
I cannot see such items spanning 2 days. Are you using the latest version v3.0.3.3 of TPlanner?