Pete are you aware that stainless has a tendency to work harden while being cut? I realize it's not like cutting butter no matter what but if you are work hardening the metal with each cutting pass you can get it to cut easier by adjusting (increasing slightly) the depth of cut to get the cutting tool past the surface just hardened from the previous cut. Basically your just trying to get past that work hardened surface material to the softer metal. Of course each pass with the cutter will repeat the hardening on the surface left after the cut is made.
This is the same for both lathes and mill. Difference with mills being the amount of material removed per end mill flute. Where you want to make sure your feed rate is just enough to get the cutter edges in behind the hardened metal. If you remove to small an amount of metal and repeatedly take cuts in the newly work hardened steel it just compounds the hardness that must be cut and wears out tooling quicker.
You may be aware of this already but I just thought I would toss it out there.