In Kirk's era, subspace messages would take days or weeks to get to Starfleet Command, and were often text or voice only (we were never sure which, because Uhura handled everything). They were occasionally out of touch, and "subspace relay stations" were plot points once or twice.
I never really noticed that feeling of being Out Of Touch in Enterprise. Maybe they were just closer in than Kirk's ship, and the basically-similar technology didn't have a significant lag time. On the other claw, it might be simply that I haven't seen that much of the show (which is something of a danger in this whole exercise).
Remember in Forbidden Planet, where they had to dismantle their hyperdrive to send a message back to Earth? If the subspace radio in Enterprise were only a little more convenient than that, it would have been a terrific dramatic hook. Apply the Wave Motion Gun effect to the communications system: if you divert all the warp drive's power for several minutes, you can just barely create enough of a warp to squirt a brief text message back to