Why does my invert sugar always crystallize?
The crystalization is to be expected, that's what inverted sugar does. It is the same thing as with honey, which is chemically nothing but a contaminated inverted sugar. So, you are not doing anything wrong. In an inverted sugar at sucrose ratios, you will get sucrose crystalizing back out of the solution, just as you are observing now. 

If you really need it smooth, you can try changing the ratio by adding some fructose, as such a mixture is less prone to crystalizing. 

The one thing that puzzles me in your description is that you cannot get it back smooth by heating, this should in principle be possible. Maybe try adding a bit of water to the syrup itself during heating, so it can dissolve again.