Is the gravitational effect of distant galaxies lost forever? Hubble's law  is usually expressed by the equation 
$$v = H_0D$$
According to this equation, the space between us and very distant galaxies,
is expanding with a speed  greater than the speed of light $c$.
As a result the light from these galaxies can no longer be detected.
Can we also assume that the 'gravitational effect'  that these galaxies exert can no longer influence our visible universe?
Since these galaxies can no longer interact in any way with other galaxies, does this means that in a way they form their own 'universe'?
How the theory of the 'big crunch' deals with this? 
 A: The influence of gravity and gravitational waves are thought to travel at the speed of light. So what goes for light also goes for gravity.
Galaxies that we see now can already be receding at greater than the speed of light. As Thriveth says in his comments, this is the case for galaxies at redshift more than 1.4. We see them because the light we see was emitted in the past.
The edge of the observable universe and therefore the most distant that objects can be to influence us now, either through light or gravity, is some 46 billion light years away. This called the particle horizon.
There is another horizon at about 16 billion light years which refers to how far away an object can be now such that its light and gravitational waves never reach us in the future. This is called the event horizon.
The exact values of these numbers depend on the cosmological parameters and, in the case of the vacuum energy density, their time dependence. 
In an expanding, accelerating universe, these horizon distances do increase, but all galaxies will eventually reach a point where they lie beyond the event horizon and their influence will no longer be felt in the future.
Of course, a big crunch does not happen in an expanding, accelerating universe.
