Hi Mike,
I don't see the problem on my machine. MM10.2. - Windows 7
But you can set as example the ImageSize->{100,200}.
Axis3D[a_, b_, c_, d_, e_, f_] :=
Show[Graphics3D[{Arrowheads[.02], Arrow[{{0, 0, e}, {0, 0, f}}]}],
Graphics3D[{Arrowheads[.02], Arrow[{{0, c, 0}, {0, d, 0}}]}],
Graphics3D[{Arrowheads[.02], Arrow[{{a, 0, 0}, {b, 0, 0}}]}],
Graphics3D[{Text["\!\(\*
StyleBox[\"x\",\nFontWeight->\"Plain\"]\)", {b*1.1, 0, 0}],
Text["y", {0, d*1.1, 0}], Text["z", {0, 0, f*1.1}]}],
Boxed -> False,
ImageSize -> {100, 200},
ViewPoint -> {8, 4, 4}, ViewVertical -> {0, 0, 1}]
Axis3D[0, 3, 0, 3, 0, 9]