The Duration: Concentration entry of the 4th-level psychic warrior power immovability [psychometabolism] (Expanded Psionics Handbook 112) means that
The power lasts as long as you concentrate on it. Concentrating to maintain a power is a standard action that does not provoke attacks of opportunity. Anything that could break your concentration when manifesting a power can also break your concentration while you’re maintaining one, causing the power to end. You can’t manifest a power while concentrating on another one. (61)
Thus the manifester on each of the manifester's turns must take a standard action to concentrate on the power to maintain it, but the power does not normally require the manifester make a Concentration skill check to maintain it.
However, while the power's duration continues, if the manifester is subject to effects that can disrupt concentration, the manifester makes Concentration skill checks normally, with success meaning that the power's duration continues and failure meaning that the power's duration ends.
In practice, this means that the psychic warrior can take a standard action to manifest the immovability power then, so long as the manifester on each of the manifester's turns continues to take a standard action to concentrate, the power's duration continues. Attacks that deal damage to the manifester and other effects, though, may require the manifester to make Concentration skill check to maintain the power's duration, but if nothing interferes and the manifester's okay with spending a standard action each turn to maintain the power's duration, the power's duration can continue as long as the manifester wants.