Does a creature exiled with Oblivion Ring come back if Oblivion Ring is itself blinked out and back in?

Oblivion Ring has two separate triggered abilities: one that triggers when it enters the battlefield (exile a nonland permanent) and one that triggers when it leaves the battlefield (return the exiled card to play). These are independent triggers, not a linked-duration effect like "until" on an Aura.

When Oblivion Ring is blinked (e.g., with Flickerwisp or Cloudshift), it leaves the battlefield. Its leave-the-battlefield trigger fires immediately, returning the originally exiled permanent to the battlefield (CR 603.6, 400.7). The creature is fully back in play before O-Ring itself returns.

When Oblivion Ring re-enters as a new object (CR 400.7 — a permanent that has left the zone is a new object with no memory of past actions), its enter-the-battlefield trigger fires again, allowing its controller to exile a new nonland permanent. The original creature is NOT re-exiled automatically; you must choose a new (or the same) target for the fresh trigger.

This is a well-known interaction sometimes used deliberately: blink your own O-Ring to free the creature it was holding, or to retarget it at a more threatening permanent.

Example: O-Ring has your opponent's Baneslayer Angel exiled. You cast Cloudshift targeting O-Ring. O-Ring leaves → Baneslayer returns to your opponent's battlefield. O-Ring re-enters → you choose a new target for its ETB trigger (you could target Baneslayer again, or any other nonland permanent).