Sometimes in Star Trek, ships are seen firing at warp in a high-speed chase. One example was Star Trek: Into Darkness, when the Vengeance fired phasers on the Enterprise at warp, causing catastrophic damage. Another example was in DS9, when a runabout fired phasers on a Dominion fighter, destroying it. Similarly, in Star Trek: Voyager, the U.S.S. Voyager fired one photon torpedo at the U.S.S. Equinox at warp, causing heavy damage and forcing the Equinox to exit warp.
However, in the Star Trek: Voyager (which, I know, I know, is notorious for its discontinuity) episode "Message in a Bottle," the Prometheus (split into three parts) pursued a nebula-class starship (perhaps the Sutherland?) and fired on it. This time, however, the Nebula-class starship's shields are clearly up. Although it does sustain heavy damage, its hull isn't breached and torn open like in the other cases. This indicates that either shields can be raised at warp, or they weren't at warp, and I'm just confused.
Is it possible to raise shields during warp? If so, why doesn't it happen more often?