Seems like a bug to me, don't have time to dig more now. WinXP V9.0.1.0
With[{
opt = Sequence[AxesLabel -> {"x", "y"}, PlotStyle -> {Thick}, AspectRatio -> 1,
ImageSize -> {300, 300}, AxesStyle -> Arrowheads[0.05]]
},
Row[{Framed@Plot[Sin[x], {x, 4, 6}, opt],
Framed@Plot[(-5 + x)/(6 + x)^2, {x, 4, 6}, opt]}]
]

and without AxesStyle:

So as we can see, Arrowheads is making the trouble but not with every function.
Can you confirm this behaviour on other enviroments?
p.s. the solution is ImagePadding -> spec ofc, but there should not be the issue.