Why can't dark matter lose energy by gravitational waves and collapse into itself? Because of lack of electromagnetic induction, dark matter can't lose its gravitational potential energy. That is preventing it from collapsing like an ordinary matter cloud in space.
But why can't dark matter lose energy by gravitational waves and collapse into itself?
 A: It is really hard to create gravitational waves and we only see a significant amount of energy going into gravitational waves under extreme circumstances. Any obvious example of this is the black hole mergers detected by LIGO, or the first indirect detection was from the loss of energy from a pair of neutron stars orbiting each other.
So a cloud of dark matter cannot lose energy and collapse by emitting gravitational waves because it cannot generate gravitational fields intense enough to create those gravitational waves. In principle a cloud of dark matter could create gravitational waves, but the energy is so ridiculously low that no significant amount of energy would be lost even over the whole age of the universe.
However dark matter, along with any type of matter, can collapse by a process called gravitational sorting. The particles of dark matter can exchange energy with each other so low energy ones sink inwards and higher energy ones move outwards. You'll find a discussion of this in the answers to If dark matter only interacts with gravity, why doesn't it all clump together in a single point? and How can dark matter collapse without collisions or radiation?
For more on creating gravitational waves see Is it possible to produce gravitational waves artificially?
A: Dark matter was originally postulated to explain galaxy rotation curves, which needed an extended in space matter envelope to explain them. So it does collapse gravitationaly, but by the fact that its postulated extent is so large its effective density has to be low.
Evidently, if it is composed of particles , in order to be around a galaxy  it has   lost energy by gravitational interaction, but total collapse into the galaxy must take much longer, as the curves, by their existence, show.
After all look at the earth atmosphere, it does not collapse on the ground although it is gravitationally interacting with the ground, due to other forces ,mainly explained by thermodynamics, that balance the very small gravitational attraction for the atmosphere molecules.
A: Well, we do not know what it is. On top of that IF it is made of particles, the density is very very low. So, it needs a lot of time to collapses.
A: Although I believe Anna explained it very thoroughly, I will give a layman's terms.
Dark matter is postulated, we currently don't know exactly what it truly is. Although it could still be made of standard baryonic matter.
It is a theoretical concept which we cannot completely explain, the answer is essentially the fact that we don't know and we cannot fully explain its interactions due to this lack of further understanding.
