I remember in old days when I was in college and drove a very old Celica, it was not rare that a car won't start and the starter need to be replaced with rebuilt one. Now with Prius that ICE is constantly on and off, is starter an issue that it would be broken at some point?
It's a little late to be asking "Now with Prius..." given that Prius has been in production since early 2000's. Hybrids, incl. Prius, were designed from the ground up for reliable, long-term start/stop capability of the ICE. What you could legitimately question is all the non-hybrid ICE vehicles, including diesel, that incorporate auto start/stop in their current generations to improve average fuel economy numbers.
Even those don't have a traditional starter. The least powerful one used is a 10kW motor for a hybrid starter generator(HSG). The specs usually mention a heavy duty starter. I'd be more concerned with battery life form them. GM's system had a deep discharge 12-volt in addition to the starter battery to power things while the engine off. Others might just have the single battery. Mazda's start/stop doesn't use the started to refire the engine; just controlled fuel injection and combustion. IIRC, Wayne Gerdes had to replace the starter on his 2005 Accord after about 3 years or so. His hypermiling style would likely mean more starting events than what factory start/stop systems would see.
The 'starter' on the Prius is called Motor/Generator1. It varies by generation, but is about a 30 HP 3 phase AC motor, that also serves as the 'alternator'. In very rare situations, it helps power the wheels. In this photo it is the motor to the left, to the right is M?G2, also 3 phase AC, which drives the wheels and regenerates electricity from the wheels. It is about 60HP, and also varies by generation. AC voltage varies by generation as well but is often 350v to 550v.
