Accepted answer
There is no count, and 25G is why: coring is a single event, not an accumulation. A needle cores when its bevel punches a full disc of rubber instead of parting it, and that either happens on a given puncture or does not. At 25G the bore is wide enough to take a plug you can see floating, which is at least honest about itself. Technique moves the odds far more than the count does: enter at an angle, rotate the bevel, then bring it upright — that parts the septum rather than punching it. Inspect against a dark background before every draw, because the number of punctures a stopper survives is a property of that stopper and this is the only way to find it out.
The relevant detail is that for a 4 mm pen-style needle the gauge options are narrow and the choice is nearly made for you.
Drawing a viscous or foamy solution through a fine needle takes long enough that people rush the plunger, which causes more foaming. Using a wider drawing needle is the fix.
Specifically, a 30G or 31G needle through a butyl stopper leaves a track that reseals, which is why fine-gauge repeated entry is tolerable and coarse-gauge repeated entry is not.
Butyl rubber closures are specified for resealing after piercing up to a stated gauge, which is the basis for the fine-gauge repeated-entry practice.
Gauge numbers run backwards. Higher number, thinner needle.