Okay, what's the problem with that stone and what perk are you talking about, please? I have a conjurer build right now.

The short version is that Spell Absorption causes many Conjuration spells to fail when cast.
Atronach Stone - 50%
Atronach Perk - 30%
Breton racial power - 50%
The mechanics behind it are that a summoning spell is treated as a self buff. This buff can be absorbed by your own Spell Absorption which results in the spell failing and your Magicka being refunded.
It's sad because the Atronach Stone is by far the best stone for a Mage on the game and this Conjuration bug really ruins it.
An easy way to see this problem is to create a Breton, active their racial power and then start spamming a Conjuration summon. You will notice that half the time nothing is produced by it.