Depends on the wire size, wind load, and how much bending
you are willing to tolerate on the supports.
The weight of the wire between supports causes a sideways
force, even without wind loading. The greater the tension
on the wire, the less sag, but the more the poles will bend.
You can get a sense of the amount of bend by looking at how
it reacts with a flag on it in the wind. They should be better
than the top section of some of the telescoping fishing poles.
Lighter wire certainly helps - I use #26 stranded, insulated
hookup wire, although sometimes I have had to replace the
wire every couple of years, as the insulation provides much
of the strength, and some types will crack out in the sun.
Of course, when a hawk or owl lands in the middle of the
wire, that will bend the supports even more!
Feeding the loop in a corner (so the weight of the feedline
is on one of the masts, rather than hanging in the middle)
will reduce bending as well.
There are various ways that you can reduce the size of the
loop for 80m without affecting the radiation too much. The
wires can be folded (which requires more wire), or loading
coils added (again, preferably at the supports, to minimize
the weight hanging between them). It will also depend on
the reason for choosing a loop, and of that particular shape,
in order to maintain the desired qualities.
For example, by
bow-tie figure-8 loop is designed to maintain
high angle radiation on both 80m and 40m (which isn't always
the case with other loops shapes).
Meanwhile, you might consider a "back stay", as often used
on a sailboat. Basically it is a back guy to stiffen the mast
that is attached near the top, goes over a spreader of some
sort, and ties back to the base of the mast. It provides some
rear support without taking up any ground space (although
a bit of overhang if you are at a property boundary). However,
it can require quite a bit of tension, and using wire with a
turnbuckle is often a good approach. (And the mast has to
be able to support the extra downward pressure without
buckling.)
Otherwise, a prop on the inside of the corner may help since
it doesn't extend beyond the loop, although that will need to
be pretty long.