There are many occasions where saucer separation on the USS Enterprise (NCC-1701-D) would have come in handy but it was only done a few times.
Is there a reason they did not do it more often? It seemed to take only a few minutes to disconnect and a few minutes more to reconnect.
I am guessing that it was hard on the ship and would require follow up maintenance.
The TNG Technical Manual (considered a canon source of information about the trek universe) offers several reasons why separations were rare:
The USS Enterprise consists of two spacecraft systems integrated to form a single functional vessel. Under specific emergency conditions, the two vehicle elements may perform a separation maneuver and continue independent operation. The two elements, the Saucer Module and the Battle Section, are normally joined together by a series of structural docking latches, numerous umbilicals, and turbolift pass-throughs.
The latching system has been designed to accept a failure rate of 1.5 latch pairs per ten separations; in the event a single pair fails to seat properly within its passive aperture, the structural loads can be shared adequately among the other latches.
...
Should any key umbilicals or turbo paths show a failure condition at the vehicle interface, the computer will close off the affected elements at the best possible points upstream of the failure. Hardware and software failures will then be dealt with later, once the emergency situation is resolved. Crews on both sides of the vehicle interface monitor the progress of the separation sequence, and are then on standby awaiting reconnection duties.
We also see some reasoning within the show itself:
SHELBY: There's one other recommendation I'd like to make, Commander. Separate the saucer section... assign a skeleton crew to create a diversion...
RIKER: (shakes his head) We may need power from the saucer impulse engines... - TNG: Best of Both Worlds, Pt I
And finally, we see in TNG: Encounter at Farpoint, Pt I the difficulty of rejoining the ship manually. It stands to reason that a computer failure at a critical time (and let's face it, those happen every other episode) could severely damage both halves of the ship, immediately ending their mission and resulting in an embarrassing trip to the nearest Stardock so that the repair crew can laugh at you fix the ship
There were several out-of-universe reasons, largely relating to the relative expense of filming sequences, lack of models and the extra storytelling time needed to see the sequence itself and the extra scripting required to explain the rules of how separation occurs:
Though less favored by Rob Legato and Dan Curry and largely unused since the appearance of its four-foot cousin in season three, the original six-foot Enterprise model had to be hauled out of storage for the ship-separation sequence in the Borg battle, since it was the only version built in two sections. The various battle effects and Borg visuals are motion-picture quality, but again TNG struck out with the Emmys for special effects. Part 2 was nominated, but it won no awards in that category. The episode did snag Emmys for sound editing and for sound mixing, as well as a nomination for art direction. - TNG Companion
Apparently there were a number of attempts by writers to add a ship-separation sequence, all shot down by the producers.
This was an opportunity to utilize those often ignored shipboard families that Shearer initially pitched to Fontana, and it was this story that helped win her a spot on the writing staff. A subplot [in TNG: When the Bough Breaks] involving ship separation and the saucer being held hostage was phased out to focus on the main story. TNG Companion
Ironically, this tendency for the separation sequence to eat up time was actually helpful in the pilot episode in extending it to feature-length
According to Justman, both the ship separation sequence and a touching scene in which an aged Admiral McCoy meets Data were a help in filling out what Fontana had intended to be a ninety-minute script. TNG Companion
Notably, the Battle Bridge set was quite expensive to build and the studio preferred not to create sets when they could avoid it.
During the first few episodes of Star Trek: The Next Generation, saucer separation was intended to be a standard maneuver in combat situations, but was rarely done because of the costs for visual effects and for rebuilding the Battle Bridge; also, it was felt that it slowed down story-telling too much. - TNG Encyclopedia
In-universe, on many occasions the Enterprise came upon dangerous situations by surprise, so even a few minutes may be too long.
Additionally, the saucer is more vulnerable when separate, as it lacks warp capability (so if separated in a danger zone, it cannot escape danger except by hoping that nobody takes a pot-shot at it while it limps away) and loses access to the main engineering power stores (though obviously it has other sources of power) so its weapon and shield capability would most likely be decreased.
When the Enterprise crew knows ahead of time that they're heading into danger, it's a little harder to make the case, but there are still some justifications:
Reduced medical rooms and staff due to being split between the two.
The standard shape for most Federation ships is due to this being the "most efficient" for the warp bubble; presumably having the saucer gone will make the warp drive less efficient, reducing either speed or final power reserves. Both speed and power can be critical to mission success.
Cramped quarters for battle crew due to most of the living quarters being in the saucer. This doesn't matter too much for short fights but could be problematic for longer missions or even just if travel time between the "safe zone" where the saucer is left and the mission target is more than a day or so. It'd be quite problematic if your crew is no longer battle-ready by the time you get there.
