Our day is 23 hours and 56 minutes long, and slowing by an infinitesimal (but measurable) amount each year due to tidal losses.
Our day has a connection with the weather, in that the sun drives all our weather systems, so heating over each part of the globe happens every day, but aside from that, your question doesn't make much sense.
Weather changes may come at the same time where you live (on a 24 hour cycle) but here in Scotland, we still have low reliability on even a 3 day weather forecast, because the weather systems that impact the UK are so complex as heating from the sun drives various air flows.
After your update, I still cannot understand what you mean. There is slippage in accuracy, but this is counteracted by leap seconds and leap years. It has nothing to do with weather. The shortest and longest days happen when they happen and are measurable. They help us define the year.
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