1. Get your RPM up where it belongs. I'd be closer to 1,000 RPM if you have coolant. 600 if you don't, but use cutting oil.
2. Check that your tool tip is on center.
3. Ensure that you are running a light and even feedrate. .001" - .0015" per rev if you've got it. Otherwise, light and consistent hand feed.
Yep. get the revs up, way way up, and use power cross feed if you have it.
We used to buy the cheap import 'combo kits' from KBC Tools for the last shop I worked in. Like Mr. Whoopee above says, you blow an insert, usually it takes out the holder. If a holder made it through the whole box of inserts it came with, we always had a few spares inserts around, and the kits were pretty cheap to boot.
We made a LOT of shims in Al-Bronze and 17-4PH, for F-18 landing gear rigging, and assorted flight surfaces. from about .006" on up, but rarely as thick as the kerf of the parting tool. Parting was something we all got very good at! Spend a morning prepping stock, spend the afternoon parting of slice after slice, and spend the next couple days Facing off the shims on both sides, to specific thicknesses to make up a whole set so the guys could have them for their repair kits when they deployed, or so that when they came in looking to have "this" size made, we could send them out carrying it, rather than waiting.
There is a real sweet spot, in the rate of feed, when you are hand feeding, and you will know it when you hit it, it is fairly obvious, it just works, rather than chattering or loading up.