There is more to time-discretization than just the Nyquist theorem.
When you time-discretize a continous signal, you essentially turn it into a stream of impulses. One impulse for each sample. To turn this stream of impulses back into a time-continous signal, you need to low-pass filter it (at least mathematically speaking). Imagine it like the low-pass filter bluring out all the spikes of the impulses, but keeping the general form of the signal intact.
You can show, that if the highest frequencies in the original signal were below half the sampling rate, then all the additional frequencies due to the spiky impulses are above half the sampling rate. So, (again mathematically speaking) the low-pass filter used for perfect reconstruction must let everything below half the sampling frequency pass undisturbed, but completely filter out everything above it. If you had such a filter (you can't build it) and you if you had an infinitely long sample stream (the filter is non-causal and has an infinite response, so you need an infinitely long sample stream) then you can perfectly reconstruct everything if the original signal truly never exceeded half the sampling frequency. As Olof Hedman already pointed out, exactly half the sampling frequency is the point where it breaks apart. At that point, you can no longer differentiate between phase and amplitude. But if the frequency is a smidge lower, due to the infinite amount of samples you can perfectly reconstruct it.
In practice, you can't build a perfect low-pass filter (except, maybe, if the signal is periodic?). Which means, the filter actually being used will have, roughly speaking, three frequency regions. A low frequency region which gets through undisturbed, a middle region, where the amplitudes get damped and a high frequency region where the filter blocks. And depending on the "width" of the middle region, you must keep a margin between the highest frequencies in your original signal and half the sampling rate (essentially what Aressera already said).
Also note, that sampling of a continous signal has nothing to do with the cycles in a
synchronous circuit.