While training Alchemy with Arcadia in Whiterun, once my skill reaches 33 the next time I train the gold is removed but the skill does not increase and my training sessions for the level increment as if I had trained the skill. The next attempt to train works normally, incrementing the skill to 34 but I end up paying for the point twice. I've tried this with several area transitions, training with other trainers to break up the training attempts for a given level so they're not all with Arcadia but every time I attempt to raise my skill from 33 to 34, the first attempt to do so results in a "lost" training session. I'm not running any mods.

I had a similar issue with the pickpocket trainer in Windhelm. Money was taken, but did not raise skill level or any level xp. This happened at pickpocket 32. I tried an earlier save and she trained fine at a lower level. Other trainers no problem. Her, not working. I trained a different skill and came back to her at a different level, and after some time, she seemed to work again. No idea what caused the problem, or what "fixed" it.

Had the same problem training Archery with Faendal, trying to go from 30 to 31. He took the gold but the skill did not increase to 31 instead it remained at 30 but the exp bar for Archery was maxed. Odd bug and mildly annoying. This happened on a brand new character started after installing Patch 1.4, though obviously this bug has occurred for others before Patch 1.4 was released.