In most cases, the situation you describe, “piece of solder that
just sat there, no matter how much flux and heat I applied”, sounds
more like either a contamination problem with the solder or the
pieces being soldered just were not yet at temperature.
When that happens first, just back off and apply some self-pickeling
flux to the solder and area around it. Bring your torch back and
heat normally. It should flow.
If that doesn’t work, open you flame a bit so it is soft and bushy,
re-heat the entire piece until it is an even dull red then tighten
the flame slightly and concentrate on the join and the area around
it. That should solve the problem.
I tend to agree with those who say that multiple heatings raises the
temp of solder previously applied. However, even with no scientific
data to back me up, I do not believe it adds very much to the melt
Cheers from Don at The Charles Belle Studio in SOFL where simple
elegance IS fine jewelry! @coralnut2