Imagine a sine wave. If you're at the peak now, after time t passes, you sample will be cos(ωt). It will be some error to it, but otherwise it is totally predictable. If you put your samples on the graph it'll be a sine wave, which will also have some frequency.NorthGuy
Then I don't understand why you can't take the same approach with an unknown signal? Use the delta RMS as your indication of when you have taken enough samples.
So, we have three different frequencies: data frequency, sampling frequency, and the frequency of sine wave that you would get if you would plot your data - we'll call it visible frequency. With me so far?
Unless you can control sampling frequency, your have no control of what visible frequency you get. It might happen to be very low.
An example from your post. Data frequency is 60Hz. Sampling frequency is 60.001Hz. Visible frequency is 0.001Hz.
If visible frequency is low, and you start sampling from the peak, you will be sampling the peak for quite a while and your average will be biased. Then you finally reach zero, at which point your result will be correct. But then you'll continue sampling around zero, so your result will start decreasing below true value again until you reach the next peak, and so on.
In case of 0.001Hz, you'll get correct results at 250, 500, 750, 1000, 1250 etc., but between 0 and 250 your result will be over true value, same between 500 and 750 and so on. Results you get between 250 andd 500, 750 and 1000 etc will be less than true value. To get the bias withing 1%, you'll need to continue sampling for about 50 cycles, 50000 seconds, almost 14 hours, which is next to useless.