I believe TNG addressed this once or twice, namely when the Enterprise-D separated the saucer or prepared to do so. The most specific example I can think of is in "Brothers," when Data has control of the bridge. Picard plans to separate the saucer and tells LaForge and Wesley, "[t]he saucer module should fall out of warp within two minutes."
As has been implied here already, warp speed as displayed in Trek is not simply a matter of accelerating to a certain speed and maintaining it, as would be the case with impulse power or any conventional form of propulsion. The warp engines are literally warping space around the ship, creating a bubble of subspace in which it travels. Thus, it's able to effectively move faster than the speed of light without having to physically do so.
So as soon as the warp engines were offline, I'd imagine the ability to maintain that bubble of subspace would fail. Thus, pretty quickly, you'd return to sublight speeds.