Would an advanced practitioner ever stop meditating?

Mindful living is another form of meditation (typically an advanced one), if one no longer needs to formally sit or walk in meditation... then i guess that would be that. But the way you phrased it, it seems it could be any reason.

There was a Sri Lankan monk named Balangoda Ananda Maiythreya thero, and he mentioned in one of his meetings with lay people that he had attained until Sankarupekkha-nana in vipassana meditation and if he had continued further, he could have become a stream-winner. But he didn't carry on from there because he had a wish to become a Buddha. However, he didn't completely abandon his meditation, still practiced samatha meditation and went on to achieve much higher levels in that as well.

So I think it is possible for advanced practitioners to stop doing it when they want to achieve much higher goals like Buddhahood once they reached a particular state in vipassana meditation. I don't see a reason for giving up samatha meditation though. Some illness might also be a reason for stopping meditation. There are several examples in literature how monks abandoned their meditation because of lust and also clinging on to wrong views .

Meditation has the benefit of dissolving fabrications and conditioning. So practicing this even after achieving the goal has advantage in subduing would be bad Karma giving unpleasant results.

Also an Arahat can enjoy the Fruit of Attainment by meditating.

Would an advanced practitioner ever stop meditating?

If we take the Buddha & his disciples as an example, I would say, no. I would also not see a reason why. In the texts, the jhānas are referenced as pleasant abidings here-&-now and that is what the arahats do.

"Bhikkhus, if wanderers of other sects ask you: 'In what dwelling, friends, did the Blessed One generally dwell during the rains residence?'-being asked thus, you should answer those wanderers thus: 'During the rains residence, friends, the Blessed One generally dwelt in the concentration by mindfulness of breathing.'"
...
"Those bhikkhus who are arahants, whose taints are destroyed, who have lived the holy life, done what had to be done, laid down the burden, reached their own goal, utterly destroyed the fetters of existence, those completely liberated through final knowledge: for them concentration by mindfulness of breathing, when developed and cultivated, leads to a pleasant dwelling in this very life and to mindfulness and clear comprehension."
_{-SN 54.11, At Icchanangala}

But having heard that Dhamma, those bhikkhus who are arahants, whose taints are destroyed, who have lived the spiritual life, done what had to be done, laid down the burden, reached their own goal, utterly destroyed the fetters of existence, and are completely liberated through final knowledge, are devoted simply to a pleasant dwelling in this very life.
_{-AN 9.4, Nandaka}

And how does the disciple of the noble ones obtain at will — without trouble or difficulty — the four jhanas that constitute heightened awareness and a pleasant abiding in the here-&-now? There is the case where, quite withdrawn from sensuality, withdrawn from unskillful mental qualities, the disciple of the noble ones enters & remains in the first jhana: rapture & pleasure born from withdrawal, accompanied by directed thought & evaluation. With the stilling of directed thoughts & evaluations, he enters & remains in the second jhana: rapture & pleasure born of composure, unification of awareness free from directed thought & evaluation — internal assurance. With the fading of rapture, he remains equanimous, mindful, & alert, and senses pleasure with the body. He enters & remains in the third jhana, of which the Noble Ones declare, 'Equanimous & mindful, he has a pleasant abiding.' With the abandoning of pleasure & pain — as with the earlier disappearance of elation & distress — he enters & remains in the fourth jhana: purity of equanimity & mindfulness, neither pleasure nor pain. This is how the disciple of the noble ones obtains at will — without trouble or difficulty — the four jhanas that constitute heightened awareness and a pleasant abiding in the here-&-now.
_{-MN 53, The Practice for One in Training}