Here is my 2 cents worth: Remember I am not an enamellist, but I do
live with one!
It sounds like the design of the ring is at fault as well as the 14K
alloy. Enamel has a preference for a specific alloy probably 18K
green. With the second section loosening, the third is probably not
far behind. Most practical solution (aside from returning the ring)
is to use a black epoxy type resin and create undercuts in the gold
to help keep the resin in place. For enamel to survive on an 18K ring
one would have to have dainty hands and hand movements!
Charles Friedman DDS
Ventura by the Sea