Periyazhwar and Andal did not take births again as cowherds. Pillai Lokacharya was speaking in a metaphorical and poetic way.
Pillai Lokacharya refers various pasurams of Alwars and stories from puranas, epics in his poems. All the references are not to be taken literally. He uses these to make the understanding easily using metaphors.
In the given verse, he refers Kulashekharazhwar, Periazhwar and Andal. As we already know, Kulashekharazhwar did not take another birth as a bird, fish or another bird. He wrote in his poetry that taking birth in Tirumala as bird, fish etc., is a privilege. He imposes himself as them. He wrote in his one of his poems he wanted to be a stepping stone in the Tirumala sanctum sanctorum. This is the reason the threshold in the Kulasekhara Padi.
Similarly, Periyazhwar also did not take new birth. The mention of him imposing birth as cowherd is a reference to a decad of poems in Periyazhwar Tirumozhi. In these poems, Azhwar assumes himself as Yashoda and recalls how she sung lullaby to the Lord. From Periyazhwar Tirumozhi,
mANikkam katti * vayiram idaikatti *
ANipponnAl seytha * vaNNach siRuth thottil **
pENi unakkup * piraman vidu thanthAn*
mANik kuRaLanE thAlElO * vaiyam aLanthAnE thAlElO
O, Naked manikin, Talelo,--Brahma has sent you this little golden cradle studded with rubles and diamonds, --You measured the Earth, Talelo 
vanjchanaiyAl vantha * pEychchi mulaiyuNda*
anjchana vaNNanai * Aychchi thAlAttiya **
senjsol maRaiyavar * sEr puthuvaip pattan sol *
enjchAmai vallavarkku * illai idar thAnE
This decad by Pattarbiran of Puduvai fame, where pure-tongued Vedic seers live, recalls the Talattu of Yasoda Sung for the dark-hued Lord who drank the deceitful ogress Putana’s breast. Those who recite it without a fault will have no sorrow. 
In another decad, azhwar assumes again as Yashoda and calls Lord Krishna for bath. From Periyalwar Tirumozhi
You have putrid butter and the dirt of the playfield all over you; tonight I will definitely not let you go to sleep scrabbling yourself. How long have I waited for you with oil and soap nut powder! O Narayana, hard-to-get Lord, come for your bath. 
These perfect songs of exceedingly sweet Tamil by Pattarbiran, King of ancient Puduvai town, recall how the full-breasted Yasoda gave a bath to the Lord Sri Krishna of hue darker than the deep ocean. Those who master it will have no evil Karma. 
We can see that, in the above poems, Periyazhwar is assuming himself as Yashoda and singing lullaby, calling Krishna for bath after playing in the mud etc., In these poems, he beautifully describes the physique of Krishna who is still a child.
Same with Andal too. Andal is the daughter of Periyazhwar. She is an ayonija (not born from a womb). She is found in the garden of Periyazhwar. Periyazhwar adopts her. She was fond of Lord Krishna since her childhood. When she came to a young age, she decided to marry none other than Lord Krishna. She did vrata to attain Lord Krishna as husband and sung poems called "Tiruppavai". These are 30 in number. In these pasurams, we find mentions of Nappinnai, Yashoda, Baladeva and Krishna. While writing these poems, she assumed herself living in the same village of Krishna. She imagined herself and her friends as gopis in the village. In this way, she imposed herself as a citizen of Nandavrajam. At the end of the vrata, she is married to Ranganatha (also called Rangamannar) in Sri Villiputthur.
In the 16th pasuram of Tiruppavai, Andal and other friends (gopikas) reach the house of Nandagopa and ask the door keeper to pass inside. In the 17th, she ask Nandagopa, Yashoda, Baladeva to wake up. In fact, she was in Sri Villiputhur but she recreated Brindavanam and took the darshan of them. So, Pillai Lokacharya was talking about this and not taking birth again literally.
After that, there is only one incident when she broke her silence and came alive. It is when Ramanujacharya was alive. Ramanujacharya had a habit of singing azhwar Pasurams while he was going for bhiksha. On some day, he was singing a pasuram in Nacchiyar Tirumozhi which is also a work by Andal.
nARu naRum pozhil mAlirum SOlai nambikku nAn
nURu taDAvil veNNai vAi
nErndu parAvi vaittEn
nURu taDA niRainda akkAra aDiSil SonnEn
ERu tiruvuDaiyAn inRu vandu ivai koLLum kolO
To emperumAn, who is stationed in tirumAl irum SOlai surrounded by fragrant gardens, I am offering (by word of mouth), 100 vessels filled with butter and 100 vessels filled with akkAra aDiSil (sweet po'ngal). Will azhagar (whose wealth keeps increasing day by day)
come today and accept these two offerings?
Translated by Oppiliappan Koil Varadarachari Sathakopan
In this poem, Andal desired to offer 100 vessels of akkAra aDiSil (sweet po'ngal) and 100 vessels of butter to the Lord at ThirumAlirumcholai or Lord Sundararaja. By remembering this, Ramanujacharya got worried whether Andal had fulfilled her promise of offering. He himself offered them to the Lord. When Ramanujacharya reached Sri Villiputthur, Andal was waiting for her in the artha mantapam outside of her original sanctum sanctorum. She thanked Ramanujacharya and called her "Anna" which means elder brother because he fulfilled her promise like a responsible elder brother. To this day, she is still in the artha mantapam along with her Lord. This is the incident which gave Ramanujacharya the name Godaagraja meaning elder brother of Goda.
This is the only instance where she returned from merging. She was not born again as a cowherd neither did Periyazhwar.