my guess: the power providers are some kind of accumulators themselves, and in factorio no accumulators can charge each other. thus the power providers aren't charged from normal accumulators during the night.
there are some other mods which separate electric networks, which give different priorities to power generation, etc. as a temporary fix to your factory (or maybe this should be documented and then become a feature for additional difficulty in setting it up correctly) you might try setting up a separate electrical network for the power providers which is connected to your main network by transformers or similar.
