I suspect what happens is pitching causes the object's origin to leave the "field of view", so it no longer gets rendered. It's a mechanism which prevents sprites which are behind you from being rendered, as that would be a waste of computing effort. When you pitch right up, it decides the pole is now behind you , but because it's so tall it should still be in front.
I remember a similar thing happening horizontally, in earlier versions of TFE with very large 3DOs when using widescreen mode. If you turn too much away fromn the 3DO, it disappears.
I guess its because the up/down viewing is handeled differently in software and hardware. In software its a column based viewshift on the Y axis. The tilting of the sprites dont change.
In hardware its a perspective correct method. The sprite is tilting away from the players view when you look up. The base game was never designed to do that. Its just like the flat sprites when you look directly down on items or bodies.
I am not an expert but i think it has something to do with the 2,5D nature of the game as i explained. Like many of the early 90ies 3D Shooters. That's why i hate free mouselook in GZDoom.
So, I looked into this and the issue is that it is was using the 3D camera direction to compute the Z value which obviously changes as you pitch up and down. Switching to using the 2D camera direction (essentially 3D projected onto the XZ plane) to compute Z fixes the issue. The fix will be in the next build. Sprites are culling if the Z value is less than 1.0.