Why am I not receiving income every 20 minutes?

Sadly, this seems to be treated by Ubisoft like it was an intended feature in many situations. This leaves some of the situations described in the question unexplained, but according to Ubi's solution center:

There are a number of things that factor into the bank income timer. The most important thing to remember is that the timer/counter is specific to the Constantinople map. This means that the timer will reset at certain points during gameplay (ex: when playing Den Defense, Altair missions, Cappadocia, etc). Also, the timer will reset if a mission is aborted.

One more reason to never participate in a Den Defense mission.

This happens after a certain Desmond memory sequence, but I can't tell you which one right now. The solution is to complete the next Desmond memory sequence and the money starts rolling in again.