Rich wrote:
 

To make your analogy more similar to the situation with SETI you'd have
to use bigfoot or perhaps the Lock Ness Monster.

Now, no matter how many nessie photos are shown to be fake, no matter
how many sonar surveys come up empty, no matter how many fish surveys
show too few fish to feed a breeding population of animals of Nessie's
purported size, the searches continue, with better and better equipment,
and they continue to come up empty.

At what point would an intelligent observer call it quits?

With SETI, we seem doomed to a similar situation.

There is one more problem: microwave beams have to be narrow
to provide enough energy density for distant receivers.
Stars and planets are in constant motion, so unless the ET
aims the beam at us for a long time, we will hear only a few
beeps. It will be difficult to tell if this was a signal from
the ET or a sophisticated prank. Science cannot deal with such
erratic data -- it needs artifacts which can be studied in
many ways for a long time. Even if we get megabytes of data
from a single ET, we cannot determine its veracity and we
cannot ask questions unless they understand our language.

A reusable flyby probe is a more reliable SETI method. The
probe can explore extrasolar planets and tell us a lot about
evolution of extraterrestrial life. It flies at about 0.2% of
the speed of light and takes advantage of gravity assist.
It flies so close to a star that gravity deflects its
trajectory by a large angle and guides it towards next star
flyby.