The creature is not dead, the creature is stone and is does not detect as alive. Regardless, nothing says that spell durations are ended or stop running or expiring or go into 'stasis mode'. If the target is returned to flesh before the dominate person spell's duration expires (1 day/level), they will still be under its effect. If it's been longer, they will not be. Similarly their mage armor or other spells will probably be gone as well.
Stone to Flesh wrote:
The subject, along with all its carried gear, turns into a mindless, inert statue. If the statue resulting from this spell is broken or damaged, the subject (if ever returned to its original state) has similar damage or deformities. The creature is not dead, but it does not seem to be alive either when viewed with spells such as deathwatch.
Even if it the creature was dead, there's nothing that says that spells stop working or go away. If you have resist fire on, then you die, your corpse and equipment will still be protected from fire until the duration ends. Some spell effects might be moot, like if you had fly[/i[, since you're a statue and can't mentally fly around. If you have [i]cat's grace and you die, you will still have that spell on until it's duration expires, even if your Dexterity is effectively 0 and the spell can't normally be cast on a corpse. It was cast while you were a valid target. If you get raised or revivified somehow, you will still have the spell on you.
