I seemed to have lost Faendal's archery training. I was able to take his 500 gold and then repay him for training, but after the last time the training dialog option is no longer available. Who else teaches archery?

He can only train you up until a certain level. The other 2 trainers are Aela of the Companions and there is a Master Trainer in the Thieves Guild

Oh, I thought you were referring to what happened to me a few days ago. I would click train and my Archery wouldn't go up from 20 but it would say 5/5 and wouldn't let me train again until the next level even though I hadn't actually trained anything. Yeah, go see Niruin in the Thieves Guild or Aela, like Indylavi suggested.

Thanks. Even after leveling up the archery training was unavailable from Faendal.

Faendal can take you to 50, Aela to 75, and Niruin to 100.

Ah, I'm up to 52.