What is the LOW frequency resolution rule analogous to Nyquist? If I'm analyzing a signal in the frequency domain, I know about the well known Nyquist criteria that the sample frequency must be > 2x of the highest component present in the signal.

However, there are very few references related to the lowest frequency I can analyze.    This problem comes up in a lot of natural data where we have limited windows of observation because the instruments to do so were only invented or in wide spread use in the last 50-100 years, and natural cycles can be decades, centuries, or longer.

One would think that you could analyze a component where at least one period was in the sample window, but I find because of required windowing to prevent edge effects that the signal often disappears (it depends on the phase).  I then thought it was a mirror of Nyquist and I could resolve any signal with at least 2 periods in a window, but actual analysis shows that to not be true when there's a another overlying signal whose period is similar.

I found through experiment that I needed at least 5 periods to resolve a signal where there's another signal near the same frequency.

Is there a formal way of representing this problem or a definitive reference I can use?

Would the same issue apply to wavelet analysis in the same manner?
The "limit" depends on the signal-to-noise ratio, and the nearest interfering frequency(s). 

If the nearest interfering frequency carrier is tuned 1% away, you might need (not just 6, but) 250 cycles or more to resolve the two separated frequency peaks, depending on the window and the S/N.  Whereas, a single pure unmodulated sinusoid in zero noise might be determined in as little as 3 or 4 non-aliased samples.

Also, there may be better low frequency estimators than depending on just a single non-rectangularly-windowed peak DFT magnitude bin, as using just that magnitude bin might be throwing some information about the phase of interference from the (nearby) conjugate negative frequency image that could be useful in improving frequency estimation and/or detection.