Since we can't make portals in real life, this is entirely speculation with no wrong answer, right?
So here's my speculation.
Supposing you solder the rod so well, it has as much air resistance as on the sides, eventually there would be a terminal velocity, somewhere near infinity. It would cause friction to the same air molecules, heating them up to an unbearable tempurature. I would advise not touching the rod after you let go.
If you try to squash the portals together, you won't be able to because the rod would squeeze in on itself, eventually break somewhere, and shoot out the side from part 1's velocity and smash through everything in its path for a long way.
Now putting one portal somewhere else would cause the rod to break at the exit (upper) portal because the rod can't feed itself to itself anymore. The near-infinite velocity would send out a deadly projectile shooting too fast to see, in the direction of the previously top portal.