You ask a very good question. In fact, as you suggest, the entropy of an isolated system can remain constant or decrease: it depends on the nature of its boundary.
What is correct is that for any subsystem we have examined, with any boundary we have observed or can (realistically) imagine, the entropy of the environment + subsystem must always increase.
An example is the Earth, which is essentially a closed system in that the energy it receives from space is virtually equal to the energy it radiates back into space. However, it receives low entropy energy (in the form of sunlight) and radiates high entropy energy. Over time the entropy of the Earth as a subsystem does not decrease, and it is this fortuitous circumstance which enables life to be sustained on Earth for very long periods of time -- for as long as the Sun continues to shine! However, the entropy of environment + Earth increases over time.
What of the universe itself? The only boundary of the universe of which we are currently aware is the single event which we call the Big Bang. The Big Bang created a universe in a state of phenomenally low entropy and, from all that we can ascertain, has been 'running down' ever since. It is because of this phenomenally low entropy with which the universe was brought into existence that stable subsystems like planets have been able to form on which very complex, low-entropy, structures -- life -- can form and be sustained.
This is a very curious fact, that the boundary conditions on the universe are such that a universe with such a phenomenally low entropy came into being. What of the future? Will this type of boundary condition be repeated after an eon of time? Are there other, more subtle and as yet not observed, boundary conditions which allow the universe to be self-sustaining, in a thermodynamic sense, over very long periods of time? This, of course, is not known at present.