Prayer Day is an event which occurs when the player outpost is within Holy Nation territory.
It consists of a squad of 5 High Paladins and 4 Holy Servants led by a Holy Priest, the last of which will require an audience. It‘s recommended to speak with the priest with a male Human with a copy of The Holy Flame book on his inventory. In case of lacking one, the priest will provide a copy the very first time for free. This limit is per game, not character.
If ignored for long enough, or the interaction goes poorly, they will leave and an assault will be launched shortly afterwards.
If all the available characters are female (even if they are female Greenlanders), the priest will say the following lines.
"Woman, are there no men to speak with me?
Wait... are there no men on this outpost? It is against sacred law to take up residence without brotherly guidance...
This will not do... This will not do at all. You are not welcome here... you will be removed."
The priest and his squad will then leave and an assault will be launched in 24 hours. There are no dialogue options available to the player during this conversation, and having a copy of "The Holy Flame" on the character that talks to the Prayer Day leader makes no difference.
It's also worth noting that if a skeleton interacts with the priest, they will attack immediately.
As soon as the Prayer Day is done another one should appear on the "Events" page. This event will stop happening if any of the following is true: you are an enemy of the Holy Nation, you are allied with either the Flotsam Ninjas or the Shek Kingdom, Holy Lord Phoenix has been killed or imprisoned.