things may have changed recently but if they haven't then the reason the monastery isn't storable is that if you sell or accidentally delete it then you just need to contact support they will replace it in your inventory for you
https://forum.en.forgeofempires.com/index.php?threads/can-i-get-another-monastery.31686/
the issue is covered from post 15 onwards
Just to be clear. Support is not an alternative to storing buildings. While we do try and help players who have accidentally removed a special building, we will not do it repeatedly, especially on the same building. The reason the Monastery is not storable is that it is not in the same class of buildings that the store works on.
I would also say that as a player, a 20% boost for how small it is makes it a building I have never even considered removing, even in end tech. Plus it is a one of a kind building that is only available from one specific quest. It can not be gained any other way which makes it very rare.
As i've said the monastery is a unique building so we will replace it. Maybe I've not made it clear but i don't want to say we will always do so as i don't know what changes will occur. So if instructions handed down are changed to not replace them then that's what will happen. As i understand it there's not likely to be any changes to this but there's always a chance.
That being said, as it is a unique building, I would like to be able to store it for posterity. I would up-vote the making of the Monastery storable.