A permanent rune's activated whenever its activation condition is met
A permanent rune doesn't change the duration of the spell stored within the rune to permanent; the stored spell's duration is unchanged. Instead, a runecaster (Player's Guide to Faerûn 69-71) that creates a permanent rune can activate that rune any number of times per day
The Forgotten Realms Campaign Setting says that normally a rune
can be triggered once before it loses its magical power, but it lasts indefinitely until triggered. A rune written or painted on a surface fades away when expended, erased, or dispelled.… When you create a rune, you can set the caster level at anywhere from the minimum caster level necessary to cast the spell in question to your own level. When you create a rune, you make any choices that you would normally make when casting the spell.… Whoever touches the rune triggers the rune and becomes the target
of the spell placed in it. (58)
So a rune can be triggered—either when it's touched or when it's read—only once or, for an increase in cost, a limited number of times, and then the rune becomes nonmagical vandalism. By contrast, a rune that can be triggered a number or times per day or is permanent can be triggered multiple times per day or any number of times per day, respectively.
The runecaster's description just has no option allowing—and no guidelines for—combining a spell effect from a rune with, for example, an effect like the spell permanency. Just to be clear, were the rune's effect supposed to be continuous, the chart for the runecaster's extraordinary ability rune craft (PG 70) would likely have included additional multipliers for the spell-stored-in-the-rune's duration as per Table 7–33: Estimating Magic Item Gold Piece Values (Dungeon Master's Guide 285) rather than the identical flat cost the game thinks is appropriate for a use-activated wondrous item.
(Some confusion's likely created by the layout error that lists the permanent rune's entry as Permanent [
tab] (until Spell level1 × caster level4 dispelled) × 2,000 gp, which errata leaves untouched but should probably instead be Permanent (until dispelled) [
tab] Spell level1 × caster level4 × 2,000 gp, that (until dispelled) text a reminder that instead of being permanent until triggered like most runes, a permanent rune is permanent until dispelled like all runes. Runes, by the way, are capable of being forever dispelled by a successful targeted dispel magic, unlike most magic items which merely become mundane items for 1d4 rounds. This sort of sucks.)
Thus, even if the rune itself is permanent, the effect the rune creates only has the standard duration of the spell stored within the rune. Nonetheless, even if it's not giving everyone in the party permanent divine power or whatever, the runecaster's supernatural ability improved runecasting remains a incredibly powerful ability that allows creation of powerful magic items with little DM oversight… that the DM can obliterate with a successful dispel magic.
Note: This reading also jibes with the Saintheart's excellent "Runeblaster: The Runecaster Handbook" (2009) as well as with this 2011 Brilliant Gameologists thread.