Like most everything in winemaking, the glib answer is, “It depends.” The real answer, however, is much more complex and as you intimate, experience can play a large part in fine-tuning your sugar-measuring schedule during fermentation.
During the alcoholic fermentation process, yeast cells convert the sugar in grapes (or other fruit) into ethyl alcohol and carbon dioxide. Typical starting degrees Brix would be around 25 for a typical red wine (or 1.106 specific gravity). Interestingly, the fermentation is considered complete on the Brix scale only when the fermentation drops to -1.0; this is because alcohol is less dense than water and will cause the negative reading when all the sugar is gone. Specific gravity (SG) is a little more intuitive as “dry” is considered anything below 0.995.
During fermentation, winemakers measure the density of the fermenting juice in order to get an idea as to how quickly the sugar is disappearing and how much sugar remains. I would argue that the rapidity with which the sugar is consumed (and the density is lowered) is almost as important as the level of sugar itself; the speed of a fermentation can give a winemaker important insight into how it is unfolding. Usually a 1–3 °Brix drop per day for whites and no more than 4 °Brix drop per day for reds is what I like to see. What happens when a fermentation goes from 25 to 10 °Brix too quickly? It means that the fermentation is probably hotter than it should be (fermentation gives off heat), which might cause the yeast cells to become stressed. Stressed yeast cells have a harder time completing a fermentation and can cause off-odors like ethyl acetate and fusel oils, which at certain concentrations become undesirable. Also, as alcohol levels increase, the yeast cell walls become increasingly permeable and sensitive to alcohol itself. A high fermentation temperature exacerbates this and can contribute to a stuck or sluggish fermentation.
However, let’s return to your original question. In my cellar experience, I would say that the most basic “standard” sampling schedule is twice a day — once in the morning and again 12 hours later. I recommend measuring sugar more often if you believe you will have a rapid fermentation. Conversely, measuring once a day is acceptable if you are in the first 24–36 hours of the fermentation; this is the “lag phase” when sugar isn’t measurably being consumed but the yeast cells are rapidly multiplying and getting ready to start performing. Measuring once a day is also acceptable if your fermentation is in its last 1–2 degrees Brix or approaching 0.995 SG, unless you suspect a sluggish fermentation. Then I would measure more often in order to get a handle on how quickly things may be coming to a halt. At that point I would start deploying anti-stuck fermentation tactics like adding yeast hulls and making sure the temperature stays between 75–80 °F (24–27 °C). Yeast sometimes need a little warmth to complete a fermentation while on the opposite end of the spectrum, excessive heat at the end of fermentation can exacerbate alcohol permeability and hasten cell death.
As you can see, you can follow the natural curve of the fermentation and match your measurements to how quickly your fermentation is progressing. This is where the experience comes in. If you know your Zinfandel is a runaway fermenter (and many are), you may want to measure more often during the lag phase to know right when the yeast cells start to “take off.” Then you’ll have an idea of when you might want to put extra temperature control to tame those wild horses. When in doubt, measure Brix twice a day and at the height of fermentation, if you can, do three. That way you’ll always have a handle on where your fermentation might or might not go.