Is it possible to turn common table sugar that has been dissolved in water back into its original granular form?
You probably can't achieve the size and uniformity of classic granulated sugar at home, not without finding some special equipment. But if you are OK with other crystal sizes, it is very simple.
All you have to do is to search for recipes for rock candy. It is nothing but re-crystalized sugar. Also considered to be the easiest candy to make, you'll find it in many "cooking with children" books and blogs.
The one problem may be that you are not crystalizing sugar, but a combination of fruit juice and sugar. If the juice has enough acid to invert your sugar, it might not crystalize well. You'll have to try and see.
Imagine, if you will, a cup of Koolaid. Essentially, sugar dissolved in water. Just let it sit there in the cup. The water slowly evaporates leaving gummy residue in the cup. Basically the same result would occur if you boiled the water away (only faster). Once it dissolves, you've lost the crystal lattice forever.
Even if granulated sugar merely absorbs moisture from a humid day and becomes a solid hunk in the sugar bowl, returning it to its previous consistency is difficult. You'd need to break it apart as best you can, maybe grind it in a blender to get a granular form factor.