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According to Star Wars and other questions (In-universe, how is BB-8's head adhered to his body?), BB-8's head is attached magnetically to his body.
That's fine and all, but, in Episode VIII, when Poe is attacking the Dreadnought and BB-8 is fixing the X-wing’s guns, he headbutts the control panel, extending some form of neck.
What is this? If it is a random extension arm (like his blowtorch), why doesn’t his head just fall into the ground when pushed away from his body?
This is addressed in the film's official novelisation. He stuck his head onto the top of his welding arm, then shoved the whole thing into the junction box. Meanwhile, his body was held in place by the sides of the "droid socket".
With inventiveness born of desperation, BB-8 had lowered the elevator he used to assume his station in the droid socket halfway, which required that he delete three improper-operation alerts from Black One, and rolled into the cavity of the fuselage, as close to the short in the junction box as possible.
Ignoring an improper-operation alert from his own systems, the astromech retracted his welding arm, depolarized the magnetic casters that kept his head attached to his spherical body, and used the welding arm to swing the head out and down, like a man doffing his hat. It smashed into the sparking junction box, primary photoreceptor swirling with electronic feedback.
Note that this plan was heavily counter-indicated by his own operations manual and the on-board systems manager for Black One.
This is a "tool-bay disk", this particular example appears to have an extension arm on it. From Star Wars The Complete Visual Dictionary New Edition:
BB-8's six swappable circular tool-bay disks can be replaced and upgraded with minimal reprogramming. This example is equipped with a magnetic-tipped bolt-spinner.
I haven't found anything on this particular tool-bay and the extension arm in it but it's likely it is either tipped with a magnet or it "slots" into the head piece somewhere to keep it attached.
However, also note than in this scene his head is moved forward quickly so it likely wouldn't have fallen down even if they weren't attached. And as we don't see the extension retract and his head go back on it could have fallen off as you imagine.
His head in the scene you describe is attached to one of the circular tool-base kit as support to headbutt the controls. His head is attached via magnets to his body, that's why in one particular scene from The Last Jedi you can see his head apart from his body
If you look closely to his "body" you can see different "circular tool-base kit" (the orange circles around his body). So in your particular scene, he attached his body to an arm that comes from the tool-base kit.
Just to address the whole magnet angle, extension is still possible to achieve.
If you're using only one magnet and you reversed it, it would eject his head away from his body, this is true.
However if you have one "rooting" magnet that keeps it attached to the body and then secondary "levitating" magnets, you could create a shaped magnetic field that would keep the head still attached but be able to change the height at which it sits. In fact, this is a necessity for his head to float on his body as a single magnet would cause it to stick to the surface rather than float above it.
It's a bit like attaching a rubber-band to the centre and then pushing away the edges. Through this kind of mechanics, BB-8 should have a comfortable range of head heights that they can move through.
However, the scene in question isn't achieved with magnetic extension, but (mis)use of one of his arm extensions.
