Summoned creatures are not real creatures.
It's important to notice that a summoning is not a calling. Although they are both from the Conjuration school, you do not summon a specific creature, you summon a generic specimen of that creature type. The summoned creature cannot be summoned again until 24 hours is passed, while it reforms itself on another plane.
Each conjuration spell belongs to one of five subschools. Conjurations transport creatures from another plane of existence to your plane (calling); create objects or effects on the spot (creation); heal (healing); bring manifestations of objects, creatures, or forms of energy to you (summoning); or transport creatures or objects over great distances (teleportation). Creatures you conjure usually- but not always- obey your commands
As we can see here, the main difference between a calling and a summoning is that one transports a creature, while the other brings a manifestation of a creature.
We then see further differences between the two types of conjuration, specifically about the manifestation reforming or the creature dying if killed.
Calling: a calling spell transports a creature from another plane to the plane you are on. The spell grants the creature the one-time ability to return to its plane of origin, although the spell may limit the circumstances under which this is possible. Creatures who are called actually die when they are killed; they do not disappear and reform, as do those brought by a summoning spell (see below). The duration of a calling spell is instantaneous, which means that the called creature can't be dispelled.
Summoning: a summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from, but a summoned object is not sent back unless the spell description specifically indicates this. A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can't be summoned again.
When the spell that summoned a creature ends and the creature disappears, all the spells it has cast expire. A summoned creature cannot use any innate summoning abilities it may have.
We can tell that the rules are a little vague about this. But James Jacobs also seems to support the idea that summoned creatures are not real, but manifestations based on real creatures.
Commune Spell-like Ability from Summoned Creatures
If the creature was summoned via Summon Monster spell, it says this on the spell effect:
Creatures summoned using this spell cannot use spells or spell-like abilities that duplicate spells with expensive material components (such as wish).
We can see on the spell text of Commune that it does have an expensive material component, thus summoned creatures cannot use their Commune spell-like ability. This is because summoning spells do not allow it, not because the creature may or may not have used it this week.
Components V, S, M (holy or unholy water and incense worth 500 gp), DF
For spells without components, the monster should have all their spell-like abilities available when summoned.
It's possible that there exist Conjuration(Summoning) spells that are not copies of the Summon Monster spell, and those, if their spell text does not say functions like Summon Monster or does not forbid the use of expensive spells, should allow their use. But, as far as I know, no such spells exist. All spells that summon specific creatures, such as Summon Genie or Summon Thanadaemon, also specify that they work like Summon Monster.
There are a few spells that are a Conjuration(Summoning), but does not have the expensive material clause, such as:
Calling spells are a whole new deal and allow you to use their spell-like abilities, if that's part of the contract, in some cases, and if the creature likes you enough, in others.
Spells like Plannar Ally, Gate and Planar Binding will conjure real creatures, with names and personalities, and should have all their abilities on their stat blocks available. They might also have things not listed on their bestiary (or source book) such as different equipment (axes instead of swords), different personalities (a neutral succubus?), different feats and skills, and even different classes since many of those creatures are intelligent enough to take class levels.
Example: a conjured Imp can use his Commune spell-like ability.
There might be exceptions to this, but this is the general ruling for calling spells as they have nothing that prevents them from using their spell-like abilities.
But be warned to not abuse those creatures when you conjure them, as you could make terrible enemies that will remember everything you have done to them while they were under your control.