I can't say for sure what's happening precisely in your situation, but in general: Skia has several different techniques for path rendering. It chooses which one to use based on numerous factors, including the properties of the path, but also the final (transformed) size of the path. Most of the techniques cache some amount of information on the GPU, but each technique has different rules for how it can reuse that cached information. For example: when certain paths are small enough, Skia generates a signed distance field of the path, which can be reused to draw that same path even at a different scale (up to a certain limit). When paths get larger, Skia tends to use other techniques that may involve linearizing the curves. Those techniques will require the data to be re-generated after any scale change.
One thing to note: requesting an MSAA surface will tend to speed up path rendering, and provide more consistent performance, so you may want to try that.