Conditions are persistent. Whenever you’re affected by a condition, its effects last until the condition’s stated duration ends, the condition is removed, or terms dictated in the condition itself cause it to end.
Some conditions have a numerical value, called a condition value, indicated by a numeral following the condition. This value conveys the severity of a condition, and such conditions often give you a bonus or penalty equal to their value. These values can often be reduced by skills, spells, or simply waiting. If a condition value is ever reduced to 0, the condition ends
Seems like this is up the the GM. I would rule a good night's rest would remove it, or appropriate magic.
I don't think that last line "These values can often be reduced by skills, spells, or simply waiting." is trying to say that it's up to the GM. It's just explaining how they tend to go away. With skills or spells that means things that specifically mention counteracting or flat-out lowering conditions (restoration, for example.) And when it comes to simply waiting, that's just how certain values work. They go down with time, such as frightened at the end of a round, or doomed after 1 day.
You're, of course, free to ignore this and put other ways of getting rid of it in your game, but I'm pretty sure by RAW it just kind of doesn't go away unless you actively do something that can reduce it. Fortunately, though, there's quite a couple ways to do so within the party's budget. The problem is, of course, that if you're not in a location where you could go and look for a cleric or a trained medic to attempt to get rid of the condition, then you may have to suffer through it for some time. Depending on the type of group you run this could be a fun and interesting challenge or an annoying and frustrating problem for the affected player. I'd recommend doing what you think is best for your group both in terms of keeping stakes high, but also not ruining their enjoyment because they feel they can't do anything about it. Perhaps one middle ground approach would be allowing the player to attempt the save again once per day or something like that.
A sufficient restoration spell can clear up the enfeeblement, but I expect that there is intended to have been a duration.
Another creature (cockatrice) had a similar issue where the slowed condition it could inflict didn't have a clear duration unless the creature affected by it had gone all the way to being petrified and was slowed after recovery, and a designer mentioned somewhere that they were pretty sure it was meant to be a 1 minute duration which just didn't get mentioned in the stat block. So I'd say a good assumption is that unless something specifies otherwise, assume everything does like persistent damage and ends in 1 minute by default.
I would highly recommend against that. Especially on an off-the-cuff answer from a single dev with a very specific duration. Another reason why they stopped commenting on rules, because people take everything they say as law, even if the rules conflict.
You have to take each instance on it's own. For the cockatrice it doesn't make sense for there to be no way to reduce the effect if you don't get petrified when there is a way when you do get petrified, but how long it lasts and whether you have to make additional saves for it, since that isn't mentioned in the stat-block, should be decided by the GM until an errata is made. 1 minute was totally arbitrary.
In the case of a Shemhaziane there's no listed way to get rid of it or a duration anywhere in the stat-block. That's very different. Additionally, Enfeebled tends to be easier to get rid of (as mentioned earlier a 2nd level spell reduces it), and more importantly: it's a level 16 creature, so the cost of hiring someone to help them get rid of the condition should be nothing to them if they can get to a safe place (assuming they don't just already have someone who can treat enfeebled).
Again, if it's not going to be fun it might make sense to consider changing it up for your players, but just because one thing should've had a duration doesn't mean everything should, and a Dev commenting on that one thing doesn't change that fact.