My reference suggests that D for PE is 2e-4, but even at that, the
copper loss would be ten times the dielectric loss out to 2GHz, if I
figured it right. It could be difficult to accurately determine your
k2 with such a small contribution from the dielectric. But there are
likely other mechanisms at work...

Roy mentioned the braid. I recall reading a nice article by, I
believe, an engineer with Andrew talking about various loss mechanisms
in coax due to things like braid and stranded inner conductor and
surface smoothness. The article went well beyond the usual theoretical
discussion that assumes smooth conductors and perfectly uniform
construction. I wish I could locate it again! I thought it was in "RF
Design" magazine, but never could find it again there, so perhaps it
was in "Electronic Design" or "EDN".

One mechanism to consider is the effects of a non-constant Zo as a
function of distance along the line. There are undoubtedly small
variations in the manufacturing process. Over a length of line that's
many wavelengths long, even small variations make a noticable
difference. It's not a dissipative mechanism, per se, but will show up
as line attenuation if you put the line on a network analyzer. Small,
flexible lines that are guaranteed to a close tolerance on impedance
are quite expensive.

I don't claim to have any definitive answers for this one, but hope my
comments give you some ideas where to look.

Cheers,
Tom