Lot's of threads on this. It is more than likely an issue with your mobile provider.
BI doesn't actually send an SMS. It uses your email to send an SMS message to you.
As long as the BI log file shows that the email was sent out, it is not a BI issue.
I also suspect that if you look in your email server sent folder, it will show that it sent the SMS message, but since you didn't get the SMS confirms it is not a BI issue.
More than likely, your mobile provider has implemented some sort of spam filter that blocks "auto generated" SMS messages. However, when you push the test option, that is a human generated email and the mobile provider has some sort of algorithm and analysis that can tell the difference.
Sometimes people here calling their mobile provider and complaining magically fixes it. Others have gone to another option like purchasing the BI mobile app and going to push notifications instead, or using another app like pushover as SMS has been getting problematic for some people.
Sometimes my SMS is fairly instant, and other times it may take days to get it.