Specifically, how long into the future can a single mind trick "program" a target's mind? If this is dependent on proficiency and skill, what are the longest known instances, and what are some particularly elaborate instructions?
Question inspired by Rey, so if you include her use in the answer you need not describe it in detail for spoiler reasons.
First of all, a vast majority of Jedi Mind Tricks or their variants shown appeared to be extremely short lived, by design - due to situation (they were only needed to fix an immediate problem).
This applies to both EU/Legends and Disney canon.
The only exceptions I can think of are:
Obi-Wan Kenobi re-moralized a drug dealer on Coruscant in AotC
While we don't have 100% proof, it seemingly is implied it can be permanent. At the very least, it would have definitely work till the dealer got home.
ELAN SLEAZEBAGGANO
Wanna buy some death sticks?
OBI-WAN looks at him. He moves his fingers slightly.
OBI-WAN
You don't want to sell me death-sticks.
ELAN
I don't want to sell you death-sticks.
OBI-WAN moves his fingers.
OBI-WAN
You want to go home and rethink your life.
ELAN
I want to go home and rethink my life.
In addition, Obi-Wan Kenobi's JMT on the Stormtrooper officer in Mos Eisley in ANH clearly lasted for a while, since that officer never did raise an an alarm that the droids were in he settlement.
In Legends/EU, it seems it was forever if applied properly: Palpatine's last Force Persuasion order given to Mara Jade ("Kill Luke Skywalker") lasted for years, till she fulfilled it by killing clone Luuke.
Joruus C'Baoth seemed to be able to mind-control multiple people for indefinite periods of time. But he basically broke their will so I'm not sure it counts as a JMT.
But as note above, most use cases seemed to have been short-term by design.
As a supplement to DVK's answer, I wanted to point out that there seems to be two ways to answer your question, based on the info in this question and from this excerpt of a Jedi using the mind trick to gain passage on a flight in Darth Bane Rule of Two (so I guess this is a Legends answer, although I don't think there's any difference in how mind tricks work between Legends and Disney canon).
"Did you want to fly us down, or should I?" he asked her. The words were easy, but as he said them he reached out with the Force to touch her mind. He did it gently, being careful not to cause her any harm as he planted the seed of a suggestion. Her eyes glazed over momentarily and a look of blank confusion crossed her face. "Uh . .. I'll fly us down, I guess. You can take the copilot's chair."
... As he had done with Irtanna, he gave another slight push, adding the mind-altering power of the Force to the half- truth.
The Jedi mind trick works by making the subject open to suggestion or command. The duration of this effect is active as long as the Jedi is actively using their power on the subject. Presumably an experienced Jedi could keep someone in this state for quite a long time, although as DVK points out most situations only require a few moments and one or two suggestions.
I think this is really what you're asking, and I believe the answer is as long as it goes unchallenged. Consider in real life, if someone you trusted told you they found water on Neptune, you'd probably believe them until someone else you trusted refuted that claim. Or if your boss told you not to forward them any calls because they were busy, you would obey that until they told you they were available again. What the JMT does is essentially make the subject trust you, and therefore obey/believe in whatever you tell them, and according to the linked question above, they will continue to believe/obey not because they're still under the influence of the force, but because it's just a thought stuck in their brains.
So when Old Ben tells the Stormtroopers "these aren't the droids you're looking for" the Stormtroopers believed him. They never raised the alarm because those weren't the droids they were looking for, so in that sense the trick never "wears off"; but if their officer had come over and said "Go arrest them, those are the droids you want" then the new information would probably override what they had been told by Ben. You could draw an analogy between the JMT and The Doctor's psychic paper in Doctor Who, where it gives (false) information to someone which they implicitly believe, and their mind fills in a reason to believe it.
