Throughout much of a space shuttle ascent, even a single SSME failure would have left the mission’s intended orbit out of reach and forced some sort of abort; a two-SSME-out situation would have left the shuttle unable to achieve any orbit at all unless it occurred fairly close to the time of nominal MECO, and the loss of all three SSMEs would, unless it occurred during one of a few short windows, force the crew to bail out over the Atlantic and leave the orbiter to crash. An engine failure during an RTLS abort (where the performance margins would be even tighter than during a nominal ascent - especially given that one of the main reasons for performing an RTLS abort in the first place was if one SSME had already failed) would be even worse; the orbiter would still probably have been able to make it back to land on two engines, but going down to a single engine would have forced a bailout unless it occurred either very late in the RTLS sequence or (for high-inclination flights) during a short window prior to powered pitcharound, and a three-out during an RTLS would, for much of the RTLS sequence, result in a loss of control and the orbiter subsequently disintegrating in flight. And, yet, nowhere in the shuttle engine-out and abort checklists is there any mention of attempting to restart the failed engine, despite the fact that many of the situations that could cause an SSME to fail would still leave it safe to restart - for instance, a hiccup in the combustion process resulting in a brief overheat, or a bubble entering one of the fuel lines and causing a momentary drop in fuel flow, or a failed sensor causing a good engine to spool down before the sensor could be taken offline.
Given the potentially dire consequences of an SSME flaming out, why didn’t the shuttle’s engine-out procedures call for attempting to relight the failed engine?