The mark from a Battlemind's Demand is long lasting and has no range limit after it has been established. Your understanding is correct. There is no requirement for a Battlemind to attack or stay close to the marked target in order to maintain the mark.
However, the Battlemind punishment options are only significant if you keep the marked enemy close. An enemy that gets away from you suffers a -2 penalty when attacking your allies (on an attack that does not include you), but barring a few additional powers you can purchase at higher level, you cannot do much about it. Generally to get the chance (or hold threat) of using Mind Spike, the Battlemind needs to stay as close as possible, and usually you want this, it's part of the job to control enemies that way.
Note that some Battlemind powers (and some Feats, not necessarily restricted to Battleminds) can apply additional marks, and the durations of those are typically different to the mark from the class feature Battlemind's Demand. Check the wording of the power. Usually all the other consequences of the mark are applied - such as being able to use Blurred Step.
Each of the defenders has different mark and punishment mechanics, and they affect how you play that class. The mark/punishment rules have typically been designed so the defender player has to commit something (an action, use of a single mark, staying close to enemy) in order to gain control over melee. But otherwise they vary, and they make each of the classes behave slightly differently - sometimes needing a little extra care when reading the abilities and figuring out how they work, but leading to enjoyably different tactics that work for each class.