When the clock stops, or in the case of one Toyota Corolla owner, when both the clock and radio ceased functioning, here is what was recommended that one seek to fix. Small note of caution: check your owner's manual for the location of the Yaris fuse box. I imagine it is the same as the Corolla, but to be honest I haven't gone out to check this morning.
Look beneath the steering wheel for the drop down fuse box. The fuses themselves are labeled on the inside of the lid. Replace the fuse in question and check the results. There may be some extra fuses in the box, but you should pick up some more yourself.
For more on this issue, see the Toyota Owner's Club Forum. The posting I referenced is: http://www.toyotaownersclub.com/forums/topic/4950-radioclock-not-working/
Good luck and happy motoring.
For more on the Yaris, see: http://jsbrookspresents.blogspot.com/2011/05/resetting-clock-on-your-toyota-yaris.html