The ability's success rate starts at 60%, increased by 4% for each of your levels of Invocations and additionally by (piety/25)%. The amount of MP recovered is from 3-5 per turn for 4 + random2avg(2 * Invocations / 3) turns. This is roughly equal to 4 to 4 + .66 * Invocations skill.
Prior to 0.19, Channel Magic was not based on a duration. With each use, it recovered a small amount of MP, depending on Invocations skill, and cost hunger but no piety. It was also referred to as Channel energy.