If you subscribe to the singularity theory that this subreddit is based on, then no later than the singularity. Unless for whatever reason it would be impossible in theory, which I can't see why it would be.

As soon as we can get nanomachines swimming around past the blood brain barrier. That will take some type of nanoscale printing, and a sophisticated AI to coordinate them all. I think 10 years seems like a decent guess if things start getting exponential soon

Not anytime soon. Some things can't be cured, they can only be treated.

There is no clear pathway to this, no reliable known physiological processes, it's not an engineering problem yet. It is conceivable that having a strong enough understanding of the mind to permanently 'cure' these conditions is necessary knowledge for us to build an AGI anyway.

Define cure I guess. There are already treatments showing more promise than SSRIs, but I'm not sure how effective they'll end up being. I suppose I'd expect this once we get a better handle on them, and how to treat them. Someone mentioned nanomedicine, which is a decent idea but I'm honestly unsure what breakthrough would do this. I'd probably still say I expect it within a couple decades, due to the integration of AI into R&D gradually speeding up progress into the singularity, but medical advancement tends to be delayed due to testing/approval (to be clear, this is why I say a couple decades, rather than one).

Have you tried the singularity pill? It solves everything.

You can not cure “mental illness”. You can re-wire the brain of the person… but it is rather questionable to do it without person consent… which you probably can not get from person who needs help… so this is pretty much dead end.