I have a slider that says: Off - Once - Twice - Constant.
Constant is good for 24hrs...
Alternatively you might consider removing the timer completely and hard-wiring the controls to be permanently on - a somewhat drastic solution though.
If you have those silly little pointers that run around the outside of a rotating dial, move them close together so it goes off and comes on again a few minutes later - I know it's not 24 hours - but almost what you want.
Peccavi
October 2008