Countries like Taiwan, Singapore and Hong Kong have had success
pegging their currency to the US dollar. On the other hand, Thailand,
Indonesia and Argentina have had problem with fixed exchange rate such
as instability. Why does fixed exchange rate have such different
outcomes?

Overvalued currencies are a one way bet.

This is a subject, one could write books about it, and in fact, i
wrote my thesis about it. The current wisdom is, that there are about
three reasons: 1. Unsufficient fundamentals (current account etc.),
another is uncertainty about the governement decision to keep the peg
in hard times (if there's a trade off between exchange rate stability
and unemployment) and the third is contagion, that is, contries might
not by themselves be succeptical to currency crises but may be induced
into one through hardships of their neighbours.

There about three zones in wich an economy can be with regard to
currency crises: the save zone, where fundamentals are so healthy that
nothing could happen, the danger zone, where it could go either way -
this usually is the most violent one if things go bad, because most
people will not expect it. And lastly the zone of no hope, where
fundamentals are so bad that the crash becomes predictable.