Does an equipment lose its attachment when the equipped creature phases out?

When a permanent phases out, all Auras and Equipment attached to it phase out simultaneously with it. This is called a "phased-out cohort" and is covered under CR 702.26d (formerly 702.25d). The Equipment does not become unattached — it simply ceases to exist in the visible game state temporarily alongside the creature.

While both the creature and its Equipment are phased out, they are treated as though they do not exist (CR 702.26b). Neither can be interacted with by most game effects. Importantly, the attachment relationship is preserved throughout this period.

When the creature phases back in at the beginning of its controller's untap step, the Equipment phases in with it and is still attached (CR 702.26e). No re-equip action is needed, and the equip ability does not trigger. The equipment is simply back on the battlefield attached to the creature as if nothing happened.

Note that this is different from a creature becoming phased out while already equipped — in all cases, the Equipment accompanies the equipped permanent if the equipped permanent phases out, not the other way around. If the Equipment itself were to phase out independently (very unusual), the creature would remain and the Equipment would detach.

Example: You control a Grizzly Bears equipped with Sword of Fire and Ice. An effect causes Grizzly Bears to phase out. The Sword phases out with it, still attached. On your next untap step, both phase back in and the Sword is still equipped to the Bears — no reequipping necessary.