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:
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.
If the zone winked out when the caster started making death saves, the power could not apply to the caster.