Each case will be judged on it's own merits (or demerits as the case may be), to answer the last 3 posts in general terms. In many ways it is a decision by the Check Captain to evaluate whether a fail of a particular component of a check was a temporary aberration, or part of an overall lower than required standard. If a failure of one component of the Sim check is viewed against good performance in all other areas, it is normal to re-do that particular component, and if successfully completed, pass the overall check with an appropriate note on the check report.
If a second attempt of one component of a check is unsuccessful, or there are short-comings in a number of other areas, the Check Captain has no choice but to fail the candidate on the check. In almost all cases, this will be followed by additional training (if a conversion) or retraining (if already qualified) until the candidate is up to standard. It is usually only after a number of retraining and re-check failures that a pilot's career is now in jeopardy.
Yes, Boeing737, Captains do fail checks, although the chances of doing so decline with increasing experience, and, by implication, a Captain is usually someone of increased experience. In the instance that I quoted in my initial post of the failed Captain, he was in fact a 'high profile' airman who had been Chief Pilot on his previous aircraft in the same company. He made the very bad decision to continue to submit to a series of check failures during a time of extreme family duress (his son-in-law was a foreign national, and had abducted the Captain's grand-son back to his home country). He was offered the chance to take time off to resolve the problem, but chose to continue working. I once had to fail a Captain who repeatedly lost control following engine failure at V1 - uncharacteristic of him, until it was found that he came to work on the day that his mother was dying (she did die that day), again, a bad personal decision.
A failed, but subsequently re-passed check can be a black mark on a pilot's record which may take many years to erase, but I know of several who weathered the experience and went on to become instructors and check airmen themselves in later years. In my own 40 years in the airline business, I know of only 4 people who lost their jobs after many repeated failures, very low odds indeed.
Regards,
Old Smokey