From our experience, the Mac mini as a server has been quite reliable. In our 8+ years of hosting hundred of Mac minis, we’ve seen very few issues. This is a very low percentage of failures.
Part of the reason our numbers are so good is because of the optimal environment. The temperature, power and humidity are very closely controlled.
The biggest worry is the laptop-style hard drive that a Mac mini uses. However, they tend to be quite reliable because unlike a laptop, the Mac mini is stationary and doesn’t get moved, dropped, and jostled.