I had that problem solved. Looking forward for the next update to see if, with a new ROM, the problem strikes again... Anyway, the way I solved it makes it look like it's an issue regarding the Mi Cloud/Account system, as mentioned above by Pertti Kosunen.
But I personally think that it is a problem that also concerns the ROMs, in general - I think that the Mi Cloud/Account system is not working well with the Miui ROM and vice-versa.
I mean, why is that so complicated to activate a sim card, and why should we have to send text messages in first place...? There are people sending the activation sms but it doesn't fix it; people making Mi sending them the sms, and it doesn't fix it either; and finally people who just did not have this problem at all. It is a mess really, and thats why I think the ROM is also involved - not a bug I should say, just a design problem along with the Mi Cloud/Account complicated system.
So I tried a lot of stuff along with someone from Global Mi assistance, by e-mail: as I have a dual SIM card phone, I took off one card at the time and did changes in my phone number registration on my Mi Account - making the system sending me sms in order to verify the "new" phone number. After that, I also tried to send the sms messages through the phone, allways one at the time, and because it was somehow impossible to do it, the phone asked me for the "new" phone number. After doing this complicated procedures, again one card at the time, and did it with both cards - the fact is that the sim cards became activated, both...! I realy can't explaine better - it was not very systematic.
Resuming: start by change cards, put one at the time, even a new one if you can, or another from someone else, change the phone number on your Mi Account, follow instructions, and by the end of all that change again for your own card. In the mean while you are making Mi sending you confirmation messages for those "new" cards/changes. After each procedure in your Mi account you also try to send the activation sms from your phone and if it is blocked follow the next steps until the phone asks to confirm your phone number. Thats what I did, for each card. Sorry I can't be more specific...
Just found out that, during October, November and December - when I had to deal with the SIM card activation problem - my phone sent 32 international sms messages costing almost €10,00.
#x&k='%$#!xxx... you and your stupid SIM card activation system Xiaomi/Miui...!