It's likely part instrument, part string. The E string is not wound so it has less grip than the other strings anyway. This can be acerbated by the acoustics of the instrument: some instruments show this more than others. If the E string cuts into the bridge, this will generally also have this sort of effect. My violin maker fits a bit of drum skin (no idea how he fixes it, probably some sort of glue) to the bridge at the place of the E string to avoid that.
I've tried using a gold-plated E string on suggestion of my violin teacher but it did not really make much of an improvement.
At the current point of time, I'm playing with a synthetic set of strings. They don't have the carrying power of the expensive Pirastro strings but I'm not playing large orchestra anyway. They break much less frequently and the overall response is more balanced and mellow.
Oh right: use a good, fresh piece of resin, sparingly. And wipe your strings off after playing. Sanding or knifing off a few layers will refresh your resin but it still does not preserve its original stickiness for more than a few years.
Now that I think of it, swapping out the somewhat ancient resin might have been the most effective measure I had for getting rid of the whistling E string in the long run. There are several different brands here as well with different composition. Might be worth trying a few but it's important that they have not already spent a decade on shelf so perhaps go to a violin maker for that: he should likely have enough of a turnaround on them to avoid that pitfall.