Does the shiny encounter rate ever reset?

Solution 1:

This doesn't work exactly like you seem to think it does - it's 1 in 8192 chance. That doesn't mean there's a hidden counter and that if you fight 8192 battles nonstop that one of them is guaranteed to be a shiny, it just means on average that's how many you're likely to end up with over that number of battles. It's really just one of the many randomly rolled stats that a Pokemon has - you might get lucky or you might get unlucky. There's nothing you can really do to influence this short of activities that directly alter the rate (stuff like Poke Radar) - normal random encounters will always have these odds.