I assume you want an in-wall 24-hour timer. How about a simple, mechanical timer switch?

• UltraPro 24-Hour Mechanical in-Wall, Dial Timer
• Woods 59745 59745WD 24-Hour Mechanical Converts A Wall Light Switch to Timer

From what you have said I would guess that the timer is not wired correctly.

Why not add a dusk dawn sensor to the circuit after the gfi. You still have the ability to kill the light completely with the switch inside (if you don’t give out halloween candy for Instance) but otherwise you never have to worry about the timer getting reset

Are you connecting the timer to interrupt the current before the GFCI, or between the GFCI and the lamps? I'm assuming the lamps are wired to the load terminals of the GFCI (or are they just plugged in to it?).

Right now, the switch is controlling the GFI. So, the power is interrupted by the switch when it is turned off. When I replace the switch with a timer, the GFI doesn't get power, even if the timer is on. The timers I have used in the past have an extra white neutral jumper, which is connected to all the other neutrals in the switch box. I have read online that the extra neutral leaves an open circuit, which the GFI detects and then trips.