How old is the battery? 5 years or more (or approaching 5 years) then I'd replace it. I had a similar issue and was convinced I had a drain somewhere and thought the battery looked newish (clearly because it sits in the boot as not exposed to the elements) and then I spoke to the previous owner who had the car for 8 years and had never replaced it! New battery fitted and never had any more problems..
Only bought this battery 12 months ago for another Z I had. Transferred it into this car.
