5DIII minimum shutter speed is not working

[Loswr]

Hi everyone,
I found this old post and it seems to be dealing with kind of my problem. My Canon 5D Mark III just ignores my minimum shutter speed at low ISO e.g. ISO 400.
My Max ISO is set to 12800. Instead of upregulating the ISO , it just upregulates the shutter time first. And i checked the safety shift, it is OFF. I don't know what to do. I just invested a huge sum into this camera and now such a simple thing is not working...... :'( Please help me with this issue.

To confirm, are you in Av mode with ISO set to Auto?

Sorry, I realized later that I forgot to mention this and modified my question post.
Yes, definitely: I tried both Av and P Mode. And ISO is set to Auto. And the awkward thing is, that sometimes it seems to be working after changing the minimum shutter time due to troubleshooting. But it always goes back to "not working" after some time.

It won't apply in P, only Av. As light dims, shutter speed should increase to your set minimum, and only then should ISO rise to your maximum, and after that the shutter speed will start to increase again.

What shutter speed do you have set as your min shutter in Av mode?