First of all they are not girlfriend or boyfriend that they will break up.
Do you even know who is Radha Rani?
She is female form of krishna .
According to devi bhagwat , along with Parvati, lakshmi , saraswati, Savitri , radha is part of prakriti. Radha and krishna are eternal consort. Their highest abode is golok dham , where they reside eternally. They never get separated. Their radha krishna along with gopi do ras always.
Now , why did they get separated in earth?
Radha rani is giver of bhakti of krishna. So when ladies of janakpur and various rishi and muni desired to get bhakti and love of Shri Ram , they got boon of getting incarnated as gopis of braj . Because ram avatar was Maryada Purushottam , so he could not fulfil their wish in ram avatar so in krishna leela purushottam avatar their wish was fulfilled. Since they desired for purest form of love and bhakti , that is why there was need of incarnation of radha rani .
Radha rani is lady of rasilala , without her ras cannot happen , without her consent no one can do ras with krishna , so think how would gopi have got love of krishna without her? And no one can get bhakti of krishna without her consent so think how would gopi would have got bhakti without her ?
So for fulfilling wish of gopis Radha rani came on earth and did ras and wish of all gopi was fulfilled . Gopi got what they were wishing .
When krishna left vrindavan , she did not accompanied krishna because she had already her task done .
So it cannot be said that they separated , they just completed their task and moved ahead .
Rukmini is shakti of krishna while Radha is giver of bhakti of krishna . Although rukmini and radha are same , but their task was different.
So , we can say that radha lived in vraj with krishna and then he lived with krishna as rukmini in dwaraka .
So where is break up and separation ?
Jay Radha Krishna !
Jay Rukmini krishna ji