In addition to those pointed out by
@Organic Marble, STS-27 is another notable example of a near LOCV scenario. About 85 seconds into the mission, the shuttle's heat shield was struck by a piece of ablative insulation from one of the solid rocket boosters. This resulted in one tile from the heat shield becoming completely separated from the shuttle, and damaging possibly hundreds more. Replaying the launch footage, engineers on the ground noticed the debris strike, but were unsure of the extent of damage to the shuttle, and requested the crew to investigate the damage using the shuttle's robotic arm. To the crew, the severity of the damage was immediately clear. However, since the mission was carrying a classified payload, and therefore could only send footage back to the ground via a very slow, encrypted channel, the engineers were unable to get a clear picture of the damage, and as a result dismissed the crew's concerns.
Despite the crew believing that the damage was not survivable, the shuttle re-entered safely. Inspections of the shuttle on the ground confirmed the damage, and it is believed that the shuttle survived only because the missing heat shield tile was located directly under a steel mounting plate for an UHF antenna, which was able to withstand more heat during reentry than the aluminum structural components which would have been exposed in many other locations. Also worth mentioning is that fact that STS-27 was only the second shuttle mission following the Challenger accident. Had it too led to the loss of a crew and orbiter, it would have likely led to the cancellation of the shuttle program.