In-Universe explanations
The TNG Technical Manual (considered a canon source of information about the trek universe) offers several reasons why separations were rare:
The sequence is intended to be used in "emergencies" only
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.
Separations actually damage the ship
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:
Separating the ship actually harms the ship's ability to maneuver in close combat.
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
Separating represents a potentially 'mission-ending' hazard
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
Out of Universe Explanations
In-Universe explanations
The TNG Technical Manual (considered a canon source of information about the trek universe) offers several reasons why separations were rare:
The sequence is intended to be used in "emergencies" only
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.
Separations actually damage the ship
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:
Separating the ship actually harms the ship's ability to maneuver in close combat.
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
Separating represents a potentially 'mission-ending' hazard
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
