Spiritual Weapon does not require concentration and only has a duration of a minute. When my cleric was knocked unconscious the on-the-fly decision was to keep the weapon waiting around until the end of the spell and I was able to use it again after getting back on my feet. We were wondering however if there was any overall guidance for summons - should they stay until the end of their duration even if the caster goes unconscious?
Spells will specify if they stop or somehow don't have an effect when you are unconscious. Spiritual weapon makes no such mention, so it hangs around doing nothing while you are out.
Summoned creatures for example all say:
disappears when it drops to 0 hit points or when the spell ends.
And all such spells have the concentration mechanic on them. There are no "general rules" to spells. (Save those mentioned in chapter 10) Each spell has it's own rules, outside of the "Spellcasting rules" of chapter 10.
For spiritual weapon the only rule for when the weapon is dismissed is:
lasts for the duration of the spell, or until you cast this spell again.