I've been at max Valor Rank for a week now. There's no reset option available as shown in the link.
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You reset your rank by hovering over the Quick Play playlist icon NOT the valor rank icon.
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For some items, players will need to reset their Valor after achieving the maximum possible Valor rank. This can be accomplished by: Opening the Director Going to the Crucible node Bringing the cursor over the Quickplay playlist Pressing and holding the appropriate interact button, as indicated by the in-game tooltip
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Does your controller have stick drift by chance? The SQUARE emblem is not showing up there and usually that occurs when your controller has or is developing stick drift that i have seen.