I don't have a definite answer to that question. But as I indicated to @
ThirdWizard upthread, more often than "never" would be a good start.
That frequency would determine how costly it is to make a poor choice. If a Rogue who trades away Sneak Attack (or, for that matter, a Wizard who decides he picked the wrong specialty) is locked in for 2 or 3 levels, that's too long. Retraining, to the extent it has ever been allowed historically, has been slow, with pretty limited changes at each step.
How do you use expertise dice to get reliable benefits? Via social rules. Via stealth rules. Via distraction rules. Via evasion rules (of the classic D&D variety). The same sort of way that a wizard uses Charm Person, or Fog Cloud, to avoid violence or to bring violent clashes to a close.
COMBAT reliability. I'd be fine with options that allow a rogue to use social skills to get a significant advantage in combat, but that means accepting rogues can use social skills not only on hostile, unwilling targets, but on targets actively attacking them. It also means, that PC and NPC rogues must be allowed to use the same skills - with binding results - on PC's. Just like a wizard casts Charm Person on a PC and, assuming he fails his save, the PC is bound by with the result.
Stealth and distraction? You mean like getting the opponent to momentarily drop his guard enabling a devastating blow to penetrate his defenses?

In any case, we're back to combat uses. My point was simply that an expertise die for noncombat skills does not make the rogue combat-viable.
My preference for the base rogue would be this: clerical attack and hit dice. (At the moment the attack bonus is the same, but hit dice are too low and there is no extra attack at 8th). The rogue would then rely on stealth (and resultant bonuses/advantage) to get chance to-hit onto a par with the fighter. Damage would be lower than the fighter, but that is part of a "three pillars" trade off; in social or exploration the fighter would be weaker than the rogue.
By getting rid of the d4 (bumped to d6) for HD, and bumping all d6 to d8,Pathfinder got the first half. Three BAB progressions, each linked to a HD (6/8/10, with the Barbarian the unusual d12).
Note that I also believe the fighter should not be able to trade away his non-combat abilities for better combat skills. Setting the bar that the difference should be more or less the same, and both should have significant utility in both combat and non-combat (or all three pillars, or also ranged and melee combat, or whatever we consider a significant part of the game) would be an excellent goal.
Until and unless there are other equally viable combat abilities for the Rogue, and it sounds like there will be none in the core/default, I remain with the view the Rogue needs Sneak Attack. I would much rather he got a choice of a variety of combat abilities, but the designers do not appear to be pursuing that approach, unfortunately.