I'm not a wine person here, I just brew beer, so if I say something stupid, forgive me.
I know a lot of wine brewers do certain additions when the wine reaches a certain SG, like energizer or nutrient, or another aeration or what-have-you. This is the only reason I could see constantly checking the SG.
If you're not planning on doing some sort of addition at a certain SG, relax, leave it alone, and don't even touch it for a couple weeks. I personally wouldn't check the SG until two weeks after pitching. The more you check it, the more you increase the risk of infection.
As far as the gravity not dropping for 28 hours, that's normal. You're going to have a lag period in which the yeast are growing and multiplying and building up a sufficient number of cells. The length of the lag period depends on a lot of things, but mostly the number of healthy cells you pitched, the size of the batch, the OG, and how much you aerated it. With a decently high gravity, and if you aerated it a lot, you will have a longer lag period (this is a good thing though!). It can take anywhere from 4 hours or so to 3 days for active fermentation to start, so relax!