As Compositepro says, BMI is a good choice for this sort of service temperature (180-230 deg C). The resins are reasonably tough. One example we've used successfully is Hexcel's 5250-4, which is also available as 5250-4 RTM. You're a bit limited if you need a film adhesive, though.
BMIs are about as good as good epoxy when it comes to the chemical environment, so reasonably resistant to fuel, oil, solvents, etc.
Most cyanate esters will also take this sort of temperature, but they tend to be more specialised and expensive. (They have very low out-gassing and are often used for satellite structures.)
The new benzoxazine resins also make some claims which make them look tempting, but in my opinion they've a way to go before being regarded as proven. They might well be worth bringing in to any material selection studies done.
Polyimides are really for higher temperatures than this.
There is quite a bit of composite in modern aeroengines these days. If it's stators or OGVs then leading edges need erosion protection (often PU or similar is enough, but thin metal plating or a sheet metal wrap mey be needed).
Carbon/BMI will generally behave well in HCF compared with metal. You need to keep an eye on formation of interlaminar cracks.
Static strength-wise think aluminium-ish. (But 55% of the density, of course.)
For more specific details there are of course many papers and it's worth a few hours googling. (Not entirely sure exactly what your "rotor support structure" is, I confess.)
