in my experience, beech is a wonderful wood to plane. I do find it very helpful to regularly oil the sole of the plane, more so than with softwoods. From what you’re describing, I can think of 2 possible causes:
[li]The cutting angle of your plane blade is too steep (nearing 45°). When this is the case, the blade rides on the bevel instead of cutting. An overly rounded bevel (especially towards the edge) can cause the same thing.[/li]
[li] The board of beech is nowhere near level enough for a smoothing plane. The blade simply doesn’t cut because it doesn’t touch the wood. Check the board with a long ruler, and try planing the high spots. Or better yet, come in with a scrub plane first. [/li]
It does help tremendously to have a good workbench to plane on! Since you can plane spruce and Douglas without problems, you have no excuse to start building one 😉 You will need to build one anyway if you want to progress in handtool woodworking. I speak from experience, I too postponed that build way too long. I worked on a makeshift workbench made from trestles and pallets for about half a year.
Hope this helps!