StreamBuilder does not rebuild tab

[rho-cassiopeiae]

I want to use TabContainer together with StreamBuilder. I tried an arrangement like this:

StreamBuilder(
  // ...
  builder: (context, snapshot) => TabContainer(/*...*/)
)

and also like this:

TabContainer(
  children: [
    StreamBuilder(/*...*/),
    // other tabs
  ],
  // ...
)

It doesn't work. The tab does not rebuild on new event until I switch to a different tab and back.