iPad issue with Pen tool

I cannot for the life of me seem to CONTINUE a path with the pen tool after having deselected it. Actually I'm not really sure what's going on. I've used Illustrator since 2002, so I expected the iPad version would let you continue a path by selecting the last anchor point and using the pen tool to proceed. What's more, I want to make a straight a line continuing out from the last anchor point, so naturally I hold shift on my iPad keyboard (also used the 'shift' catch-all corner circle tool thing on-screen) and when I tap to plot the point nothing happens. As if I've deselected, it just goes blank. Even when I go off to the side of the canvas with the pen tool selected to create a new path, holding shift does the same thing. Nothing. First point disappears. Blank. And get this, even when I don't use shift and create a line with 2 points to join it to the last anchor point from the path I want to continue, it doesn't. Inexplicably, it remains separate. iOS, Illustrator app, everything's updated. Hoping I don't wind up in a mental hospital from this. Why Adobe? WHY? Any help would be greatly appreciated.