HSS is hopeless for stainless steel, and so is ticn (IMHO). Use solid carbide.
I have been using 0.125 flat endmill at 0.015 DOC, 0.5 IPM (max) 3600 rpm.
If you can't run that fast use 0.15 IPM at 1100 rpm.
You must go really slow, because the side load bends the cutter. I have been going to 6mm deep with that setup. Nothing broke in 10 hours.
For thin things I would just get a dead 1/8" broken very short carbide drill and grind it dead flat on the end.
The dead flat grind is for using the drill for a mill in THIN SHEET.
With the thin sheet I assume you are cutting slots. Easiest to pre-drill a starting hole. At edge of sheet advance at 10% of your normal feed rate until fully engaged both sides. The job supports the side loads.
For thin sheet I just drill through, and then use the drill drill as a milling cutter up near the end of the flutes.
Lots of flood coolant with soluble oil to clear the chips. The chips will break cutters.
When plunge milling, if you must, you must not ramp down in Z more than about 0.01" per inch. Any more will bust the cutter.
You need a slot mill grind to achieve this. I just sharpen broken drills for this.
You need a CBN or green grit wheel. Look at a slot mill and copy the grind shape used.
A good source of broken/blunt drill bits, this size is your local PCB manufacturer. Ask them to throw all the old bits in a box for you.