Perhaps because, from the moment Alberich's caught, his hands are tied, so
he cannot reach the ring, as he seems to need to. Only when he agrees to
the ransom, and sends his command to the Nibelungs, is he allowed to get
at it again. So that, one guesses, would be the time to use its power. In
productions by Scottish Opera and ENO, among others, Alberich was
thoroughly trussed up as Wagner intended, with only one hand freed to
wield the ring, and Wotan had his spearpoint at Alberich's throat
throughout. 

Or, for the same reason it couldn't protect either Fafner or Brunnhilde
from Siegfried. The ring never had that kind of power.  Deryck Cooke,
in 'I Saw the World End', asserts that the Ring was only good for
finding wealth, i.e. gold.  Alberich uses it for that purpose in 'Das
Rheingold', and that is the reason Wotan wants it so badly. The power of
the ring isn't a direct, blow-them-away kind of power, although
obviously it can help him create such things. It cannot destroy rope or
chains, or make them come loose. 

Further, it might be that the ring (like the magic fire, or Wotan's
spear and the rule of law that it represents) does not have any power,
except over those who believe in it, or fear it. Therefore it does not
have any effect on Siegfried, who never learned (or has forgotten that 
he had learned) fear. If Brünnhilde had been a little smarter, she would 
have realised from this that her captor was Siegfried in disguise.

In 'The Perfect Wagnerite', G.B. Shaw compared Alberich to a capitalist
and, in one of his late essays, Wagner himself compared the ring to a
"stock-exchange portfolio". Dieter Borchmeyer has commented: "This
comparison underlines the abstract power of an object that cannot be
used in acts of physical violence, which explains why it can repeatedly
be wrested from whoever happens to be wearing it... the ring grants its
wearer power over the world only because it is a symbol, albeit one
grounded in myth and magic. As the abstract basis of the possibility of
accumulating capital, the ring may be capable of allowing its wearer to
win 'the world's inheritance' and 'measureless might' ... but it can be
stolen from its wearer with a minimum of cunning and force, just as any
artful dodger can steal money, checkbooks, documents and credit cards
from the most powerful capitalist in the world if the latter carries
them around with him or her unprotected." ['Drama and the World of 
Richard Wagner', tr. Daphne Ellis, Princeton, 2003, pages 171-2.]

Although the 'Ring' is most often interpreted in terms of a conflict
between love and power, this interpretation is not universally accepted;
and many of those who do see the cycle in those terms, also acknowledge
that it is not only concerned with this conflict.  It is possible that
Wagner was primarily concerned with love and power when he wrote his
libretto; it is certain that his own understanding of that libretto
changed after he had become a disciple of Schopenhauer.  Therefore it
might be an oversimplification to regard the ring as a source of power,
or even as a symbol of power.