If possible: move to digital
My first thought is to move to digital: make digital scans or photos of your slides and use a digital projector and a laptop. One of the risks of a projector running 24x7 is overheating, with the possibility of a fire breaking out. Please be aware of that.
Also take into account that you'll need to frequently change the light bulb if you rely on the classic incandescent light bulb.
Ballpark figure: ~12 hours of illumination per slide
Researching into your question, I stumbled on this Tate Resesarch article on the conservation of slides. It is full of details and background stories. Highly recommended reading material. The introduction states:
With slide sets needing to be changed roughly every six weeks, a large number of duplicate slides needs to be provided for every slide-based work.
A rough calculation, based on a fully loaded carroussel of 80 slides, this is around 6 weeks * 7 days/week * 24 hours/day / 80 slides = around 12 hours of projection time per slide. This assumes 24x7 illumination, but also assumes a full carroussel. So this gives you a ballpark figure. You'll want to duplicate your slides long before that.