Gene,
1/8" is very small and super easy to break...period!
HSS is tougher and more forgiving than carbide.
Watch your backlash if milling a pocket...maybe the tool is climbing when you reverse directions due to slop in the slide. You can tighten/lock the slide just before reversing to help prevent this. Also, take lighter cuts... if you are milling the full 1/8" width, go .020"-.050" deep per pass. The corners on inside pockets can always be tough.....patients, patients, patients!
Excessive chips can jamb the tool and break it....keep the chips clear and lubricated to prevent/reduce recutting and jambing.
Generally I prefer 2 flute mills for deep pockets/slots that have very little room for chip evacuation. 4 flutes on outside/perimiter work.
In a manual mill, it takes a gentle touch and experience...when in doubt, go slower and lighter.
Good luck,
Rob