An example of the decision your talking about happened a few miles from my house at New Smyrna Beach (EVB) airport. An F-4U
Corsair, owned by Collins Foundation and newly restored was being test flown by veteran airshow pilot Dale Snodgrass. The right main gear refused to extend. Dale tried maneuvers in the air and additionally bouncing the plane off of the left gear to try to get the gear to extend. After exhausting all options, he retracted the left gear and opted for a belly landing. Because he shut down the engine prior to touchdown, and because of the Corsairs unique gull wing, little damage was done to the aircraft and it was repaired.
As a side note, and ironically, a pilot was forced to ditch that same F-4U
back in '97 after running out of fuel. It was after years of restoration that Dale was taking it up for its first flights when the gear incident happened.