TL:DR at the end.
Quick background: An SMS Short Code is 5-6 digit phone number that is used by businesses to send text messages. Some businesses use SMS Short Code messages for security. Dropbox is one of those. They offer a two-factor authentication method in which you log in with a username & password, then they send a text message from Short Code #732873 with a security PIN to finish your login.
I recently switched my phone to T-Mobile, and selected the Simple Choice plan, a month-to-month no-contract plan.
Next time I tried to log in to Dropbox, the app prompted me for a code that hey had sent via text. No text message. Tried again and again. No text.
Contacted Dropbox support, but for some reason they're fixated on sending a text code. Round and round, they wouldn't budge from requiring the code they sent - which I wasn't getting.
While that was going on I was calling T-Mobile support and getting the party line from them: "There's no text message block on your account, sir." They implied that Dropbox was screwing up. After several troubleshooting calls they escalated my problem, telling me that tech support was researching and would get back to me in 2-3 days.
Googling the issue repeatedly, I finally found this interesting line in a T-Mobile Support chat thread: Simple Choice No Credit Check accounts are restricted from receiving premium services and short codes.
So, I call T-Mobile again, this time responding to "There's no text message block on your account, sir" By saying: "I just found out that T-Mobile is blocking SMS Short Codes, and because of that I can't log into my Dropbox account. I need you to clear the Short Code block."
At that point I reached a service tech who fixed the problem in two minutes.
Why T-Mobile blocks Short Codes from Simple Choice No Contract customers is a question no one at T-Mobile could answer. They will enable it if you ask, but only if you ask the EXACT RIGHT QUESTION.
TL:DR T-Mobile blocks Short Code messages for Simple Choice No Contract customers, but only their 2nd level tech support seems to know this. To fix this, call T-Mobile, tell them that some service is sending you a PIN via Short Code and ask T-Mobile to un-block Short Codes.