Zone cast by a player disappear when the player goes unconscious/dying?, or only if they actually die?
When they actually die
'Dying' is a different state than the moment the character actually 'dies'. Pg 260 of the Rules Compendium makes it clear:
Dying: When an adventurer's hit points drop to 0 or fewer, he or she falls unconscious and is dying. Any additional damage he or she takes continues to reduce that current hit point total until the adventurer dies.
However, as Oblivious Sage pointed out, zones that require an action to sustain them will fail to be sustained if the character is unconscious. Zones that last encounter long will continue until the encounter is over or the creator actually dies, whichever comes first.
Something to note is that if zones were deactivated by near-death experiences in this way, the wacky hijinks that revenants (and similar races that have weird death-saving conditions) can get up to would be rather limited.
Further evidence can be seen in the Shaman Level 22 Attack Power Life and Death Struggle.
Life and Death Struggle You anchor your allies’ souls to their bodies, keeping them from shuffling off the mortal coil for a short while.
Daily Healing, Primal, Zone Standard Action Area burst 2 within 10
Effect: Each ally within the burst can spend a healing surge. This burst creates a zone that lasts until the end of the encounter. While within the zone, you and your allies gain a +5 power bonus to death saves. Enemies within the zone cannot heal or regenerate.
If the zone winked out when the caster started making death saves, the power could not apply to the caster.