Few people seem to understand that this trope only applies when you're actually in the event horizon, the actual black hole where light cannot escape. Keeping a large distance away from the black hole's centre can, in fact, sustain orbit, as long as the orbiting body does not stop orbiting and continues to generate centrifugal force. No centrifugal motion and the gravity will suck.
The trope stems from a naive Aristotelian view of gravity, coupled with Space Friction. After all, a baseball falls to the ground, so do asteroids; why shouldn't a spaceship?
If the ship is moving at any significant speed relative to the planet, in a direction other than straight up or straight down, its momentum will carry it past and create a centrifugal motion that balances against gravity. This is an application of Newton's First Law of Motion (Inertia): an object will not move unless a force acts upon it, but also an object will keep moving unless a force acts to counter it. The spaceship will continue to revolve around a planet as long as it never stops revolving. If it stops, then this trope applies. This is why the moon doesn't crash into the earth, because of such centrifugal forces balancing the centripetal pull of gravity - as The Hitchhiker's Guide to the Galaxy tells us, flying is simply the art of throwing oneself at the ground and missing...
Despite this, fictional spacecraft have the nasty habit of plummeting from the sky like bricks the moment their engines go off-line.
A related subtrope involves a spaceship trying to escape a Black Hole or other gravitational Big Bad by pointing the ship straight upwards, with the implication that it will fall back and be destroyed if the fuel runs out or something breaks. A more sensible approach would often be to thrust laterally, setting up a stable orbit and buying the Good Guys time to fix things. But that's not as dramatic, is it? note
The only two situation in which this trope might be justified is invove a satellite passing through the atmosphere and the theoretical example of a statite. If a satellite is currently in an orbit that would take it within the atmosphere of a planet and it lacked the means to sufficiently change its orbit such that the path no longer intersects the atmosphere. In this case, the orbit would decay, getting smaller with each time around the planet until it eventually crashes. What causes this is not the gravity, but rather the friction of the satellite passing the atmosphere slowing it down and reducing its angular momentum. This is how aerobreaking works, but is only usually attempted when the means of altering the orbit (aside from the atmospheric friction) is possible.
A statite (aka stationary satellite) is a hypothetical type of satellite that doesn't orbit but uses some kind of force to "hover" over a planet, counteracting the gravitational pull. A proposed example would use solar sails to hold position over the Earth, redirecting the sun's energy to oppose the gravitational force pulling it down. If something were to happen to the sails so that it couldn't oppose the pull of gravity any more, it could indeed plummet toward the planet.
The statite example in a science-fiction context provides an explanation for Gravity Sucking. If a ship, let's call it the Enterprise, was in a powered orbit, losing power could cause it to come crashing down. For instance, if it was holding position over one spot on the Earth's equator, but was at the orbit of the International Space Station (orbital period 92 minutes) instead of geostationary orbit (orbital period 24 hours), its orbital velocity would be nowhere near sufficient to maintain that orbit if the power goes out, causing it to be pulled down.