Hi Gargy
I, too, had the dye (called a hysterosalpinogram, spelling could be off, or HSG) done on the 22nd Dec. One tube flowed really fast and spewed out the end while the other one seemed stuck. They kept forcing the dye through and eventually it did. The pain while they were doing it was immense but I kept focused on the end result, being to get my body working to make babies. I get my results of my HSG on 23rd Jan, but am pretty certain that the dye did remove a blockage. I would imagine that they can reoccur because the dye is only a temporary measure. It's purely to see how your tubes are, removing blockages is a side effect. I've also been told that falling pregnant can also occur more easily after a HSG because the dye cleans everything out.
Good luck.