How can I prevent the cocoa in my hot chocolate from solidifying over time?
Apply heat.

It's not quite what you were looking for, but it's probably the only solution that won't involve adding chemicals.

Basically, a set amount of milk can hold a specific amount of chocolate in suspension. The hotter it is (below boiling), the more it can hold. That's why as the milk cools, the chocolate it can no longer hold falls to the bottom of the cup.

The three options are:


Keep it warm, by using a mug warmer (like Catija suggested). If it doesn't cool, it won't lose the ability to hold the chocolate.
Start with less chocolate, that way, it won't be too much for the milk when it's cooling. Obviously, this will affect the flavour.
Add chemical additives, like emulsifiers, which will allow the milk to hold more chocolate.


As I said at the beginning, I think the best option is the first one. Apply heat.