Can anyone suggest a suitable material from which to make an
ultra-flexible mobile whip antenna say about 3 to 4 feet long. I need
something that can be bent to 90 degrees at a very small radius and
still return to reasonable straightness.

Sure, get some 1/4 inch fiberglass rod, loosely helix some #22 wire up the
length, and secure with some heat-shrink tubing. You can bend this into a near
circle.
73 Gary N4AST