I was able to replicate this issue in Flash CC on OS X 10.6.8 when drawing with the mouse. The point at which the brush stops drawing is consistent too, until you use the hand tool to adjust the stage position. Then the brush stops in a new place.
I got the same issue with a 128 x 128 document.
The issue was gone with a 256 x 256 document.
A possible work-around while you wait for Adobe to fix the issue would be to work at 256 x 256 and scale your content down to 64 x 64 when you're done.
Just want to update you all that the latest Flash CC 2014 release(188.8.131.52) has the fix for this drawing issue.
This release also features
* New and improved Motion Editor
* SVG export
* WebGL for animation
* Variable Width Tool
* Tweening for variable-width strokes
* Object-level Undo
* Export as Projector
* HTML5 extension support
and much more...
To know more about what's new and exciting in Flash CC 2014, please visit
Flash CC 2014 Overview : Animation software | Download free Flash Professional CC trial
Flash CC 2014 Blog Post : http://blogs.adobe.com/flashpro/2014/06/18/flashprofessionalcc2014/