QtCreator fails to build/run projects due to "Too many open files"

In a multi-product project setup using QBS as build system, QtCreator fails to build or run any project parts after some time.

There is an error in the Issues tab which reads:

:-1: error: Failed to start process launcher at '/path/to/Qt/Tools/QtCreator/libexec/qtcreator/qbs_processlauncher': Too many open files

I don't know which open files QtCreator is referring to. I tried closing all open code editor documents which had no effect. Closing and reopening QtCreator works, until the error reappears after a few application runs.