Stardates aren't supposed to work. The makers of the original series didn't want to pin down exactly how far in the future the show took place, perhaps because they knew how unwise it was to try to predict how quickly technology will advance. While the majority of references seemed to put TOS 2-300 years in the future, at least one episode ("The Squire of Gothos") had references putting it more like 700 years ahead. So stardates were just placeholder numbers, something put in to make it sound like a date had been mentioned, without conveying any actual chronological information of any kind. There was a general trend for the numbers to increase over the course of the series, albeit inconsistently so, and in The Making of Star Trek
, Roddenberry offered a handwave explanation about how stardates are calculated differently depending on where you are in space, how fast you're moving, and so on, to explain why a later episode could have a lower stardate.
Even in a single story, the stardates can be wildly inconsistent. In Star Trek: The Motion Picture
, you can work out roughly how much time passes between the different stardate references, and they range from under 4 hours per stardate unit to about 32 hours per unit.
When TNG came along, they adopted a practice of treating each season as 1000 stardate units long -- the first season was 41xxx, the second was 42xxx, etc., so if you assume that each season is exactly one year long and begins on January 1, simple arithmetic gives you the stardate scheme used at this site
and favored by Pocket Books in its ST novels. Yet the scheme used in the 24th-century shows was never entirely consistent. TNG's first season started off increasing the numbers after "41" steadily, but then, perhaps due to all the staff upheavals, they stopped keeping track and the order became random for most of the season. After that they appointed the script supervisor to make sure the stardates went consistently upward from episode to episode, but there was no attempt to work out any consistent intervals; one episode might increase the numbers by roughly one per day, while another might increase them by six or ten in the course of a day. I don't think they ever really made any effort to stick with the 1000-units-per-year thing, which would make each day about 2.7 units, when it came to the last few digits.
("Pen Pals" is an interesting case. It's meant to span nearly eight weeks and the stardates go up by about 45 units, suggesting it might be around 1 unit per day. And every one of the log entries in the episode ends in ".3," suggesting that Picard always records his log at the same time every day. But that was only in that episode, not afterward.)
And there are episodes whose calendar dates are given or at least suggested, and their stardates don't fit the scheme I linked to above. So despite being slightly more orderly than TOS stardates, TNG/DS9/VGR stardates were still meant to give only the impression of the passage of time rather than containing any real date or time information. And DS9 and VGR (especially DS9) used them less and less as time went on.
The 2009 movie tried to simplify things by making the stardate just the year followed by the number of days into the year, but that has its own problems, like being Earth-centric (as if the "starts on January 1" scheme isn't) when the original suggested something more universal, and also lacking in detail if the smallest interval it measures is a whole day. But I've learned that it's best not to try to divine any real meaning from onscreen stardates. They're not meant to mean anything -- just to sound like they do.