Do you have the Seasons EP? If you do, then that is what is going on. When Seasons is added, plants now will only grow in certain seasons. Hover your mouse over the plant and it will tell you which season it grows in. One thing you can do is plant them at home and shelter them, this means put a roof over them. They don't have to be surrounded by walls, but a Green House does look nice. Once they are sheltered, they will grow, and be harvestable every day.
Oh yes, one last thing, now your sim has to be in the same area as the plant at 5 a.m., that's when all the stuff for the plant happens. If you miss the 5 a.m. time, you won't see anything happen.