How long before the end of my Non-O Visa 1-year extension should I apply for a renewal?

There is no condition you HAVE TO apply for a new 1-year extension within x days. You can apply for one even on the last day of your current extension.

While, how early you CAN apply for a new extension varies on immigration offices. Bangkok, Chiangmai and s few other immigration offices allow you to apply when you have 45days or less with your current stamp. Others allow you with 30days or less remaining.