Let me first focus the question on mold only, and not consider stain since stain can be either chemical (enzymatic) or biological in nature. Mold is a fungi and must have 4 things to survive and grow: 1) food (the wood) 2)oxygen 3)favorable temperature, and 4) moisture. The optimum temperature range for many fungi is 75-90 F. The moisture content must be above 19% for fungi to grow. Both moisture content and temperature are the primary determining factors in the growth of fungi in wood.
I do not have data that states "we find more mold in the months of A and B". So please allow some conjecture based on what we know. Excessive wood moisture might be present due to 1) incomplete drying 2) rain rewetting of dried lumber that has been improperly stored. Depending on geographic location, the climate during certain months might result in high outdoor EMCs (equilibrium moisture contents) that retard air drying, but generally these average EMCs are below the threshold required for fungus (>19%MC). The point being is that should the lumber be rain wetted in a high humidity month (e.g. July - Sept, depending on location), subsequent warm and humid days will encourage fungal growth. Based on these facts, I suggest that the worst months of the year for mold (admittedly depending on location) are July through September, on average. Of course, other factors such as whether the lumber is stored in a warehouse (heated or unheated, closed or open, etc) or outdoor storage are certainly big factors.