I think the mame default is 25% I'd try 35% to start with and fine tune it from there
your not using a U360 by any chance are you?
No. It does it either with XBox 360 pad or Seimitsu LS32.... on two different machines.
EDIT: I just tried Bender's idea on my desktop PC whicj just uses an XBox 360 pad and Mame-UI. It worked! Well... I played a quick couple of games of DK and reached L=05 and it didn't do it once. The default setting in Mame-UI was 30% so I upped it to 50%. Everything played just the same as before except that little annoyance was gone. I'm gonna leave it at 50% and try that setting on my other projects and see how they go.
Thanks Bender 
No problem, I've had similar issues with analog sticks like the Xbox360 controller, but....
Man, that's wierd that it would do it on micro switch stick (Seimitsu) my understanding is that it's just for analog, but hey, if it works
on that machine I'd make sure mame wasn't trying to put an analog map on that digital stick

under mapping it defaults to "auto" which I might turn off for a digital stick, although I guess that brings up issues between 4-way and 8-way
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