I have drilled a few holes
I have drilled a few holes where the core bit fills with glass quickly. The smaller bits are the worst have to have the core cleaned out reguarly or it will not drill well. Sometimes a piece of glass will get stuck at the very edge of the bit and prevent drilling. I am not sure why you can not see the hole you have started drilling but perhaps you can mark it with a crayon to help you see it.
I would start the drill at lowest speed before inserting it back in the hole since will help prevent the bit (and glass too) from breaking and prove to be an easier start. A core bit should be able to drill its length as long as it is kept clean. Also take in mind that these bits loose their cutting ability when the diamonds start to wear. I believe my last bit wore out after about 20 holes, maybe less.
High rivers and clear skies