There is nothing wrong with breaking up a single verse over two rak‘ahs, but that is contrary to what is preferable

It is permissible for the worshipper, after reciting al-Faatihah, to recite part of a verse, especially the lengthy verses such as the verse on debt. There is nothing wrong with breaking it up and reciting it over two rak‘ahs. There are several texts which indicate that. 

Firstly: 

All of the Noble Qur’an is the word of Allah, may He be exalted, and in all of its sentences and words there is reward and virtue. Whoever recites a few words of it, or some verses, has recited something of the words of Allah, may He be exalted, and will attain the reward for that, by Allah’s leave. Allah, may He be exalted, says (interpretation of the meaning):

“So, recite of the Quran as much as may be easy for you”

[al-Muzzammil 73:20]. 

It was narrated that ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever reads one letter of the Book of Allah will have one hasanah for it, and each hasanah is a tenfold reward. I do not say that alif-laam-meem is a letter, rather alif is a letter, laam is a letter and meem is a letter.”

Narrated and classed as saheeh hasan ghareeb by at-Tirmidhi; classed as saheeh by al-Albaani in Saheeh at-Tirmidhi. 

Secondly: 

Many verses include a number of complete and independent meanings, which makes each one of them suitable to be recited and reflected upon by itself, such as the verse in which Allah, may He be exalted, says (interpretation of the meaning):

“So unto this (religion of Islam, alone and this Quran) then invite (people) (O Muhammad SAW), and Istaqim ^[1], as you are commanded, and follow not their desires but say: “I believe in whatsoever Allah has sent down of the Book (all the holy Books, this Quran and the Books of the old from the Taurat (Torah), or the Injeel (Gospel) or the Pages of Ibrahim (Abraham)) and I am commanded to do justice among you, Allah is our Lord and your Lord. For us our deeds and for you your deeds. There is no dispute between us and you. Allah will assemble us (all), and to Him is the final return”

[ash-Shoora 42:15].

So if a person recites part of this verse with a complete meaning, for example, there is nothing wrong with that. 

Thirdly: 

There is no report of any prohibition on breaking up a single verse or even on breaking up a single soorah. As no such prohibition has been narrated, and the general basic principle indicates that it is permissible, the ruling on that is that which is indicated by the general basic principle. 

Fourthly: 

In the words of the fuqaha’ we find that which also clearly indicates that this is permissible. 

Ibn al-Hammaam al-Hanafi (may Allah have mercy on him) said: 

If he recites half of a lengthy verse such as Aayat al-Kursiy or the verse on debt, it was said that it is not permissible because it is not a complete verse, but the majority (of scholars) are of the view that it is permissible… This was stated definitively by al-Qadoori, who said: The correct view according to the madhhab of Abu Haneefah (may Allah have mercy on him) is that whatever may be called Qur’an is permissible. This is also the view of Ibn ‘Abbaas, who said: Recite whatever you have learned of Qur’an, and nothing of the Qur’an can be regarded as too little.

End quote from Fath al-Qadeer, 1/333 

An-Nafraawi al-Maaliki (may Allah have mercy on him) said: After reciting al-Faatihah, you may recite – as it is Sunnah – something from the Qur’an, even if it is a short verse, such as “With spreading branches” [ar-Rahmaan 55:48] and  “Dark green (in colour)” [ar-Rahmaan 55:64], or part of a lengthy verse such as the verse of debt. But it is preferable to recite a complete soorah.

See: al-Fawaakih ad-Dawaani, 1/178; Haashiyat ad-Dasooqi, 1/242 

Ibn Hajar al-Haytami (may Allah have mercy on him) said: 

One may attain the Sunnah action with less than a verse.

End quote from al-Minhaaj al-Qaweem Sharh al-Muqaddimah al-Hadramiyyah, p. 99 

Al-Bujayrimi ash-Shaafa‘i (may Allah have mercy on him) said: 

If he recites part of a verse, he will have attained the Sunnah action, and that is acceptable if it conveys a complete meaning, such as a short verse that gives a complete meaning.

End quote from Tuhfat al-Habeeb ‘ala Sharh al-Khateeb, 2/68 

Al-Mardaawi al-Hanbali (may Allah have mercy on him) said: 

The correct view is that reciting a soorah after al-Faatihah in the first two rak‘ahs is Sunnah. This is the view of our companions… It says in al-Furoo‘: What appears to be the case is that even part of a verse (is sufficient), because of the apparent meaning of the report.

End quote from al-Insaaf, 2/120 

Fifthly: 

However, we say that this action is contrary to what is preferable, because a single verse is discussing one topic, and the words of this verse are interconnected, so breaking it up usually leads to an incomplete meaning and damaging the context. Hence the early generations regarded it as mustahabb (preferable) to recite a complete soorah, and to avoid breaking it up in more than one rak‘ah. So it is more apt to say that this is also preferable with regard to a single verse, even if it is lengthy. It says in the saheeh hadeeth – about the story of the Ansaari who was struck by an arrow (shot by a mushrik) when he was praying –: When the Muhaajiri saw the blood of the Ansaari, he said: Subhaan Allah! Why did you not alert me the first time he shot (the arrow)? He said: I was reciting a soorah and I did not want to interrupt it.

Narrated by Abu Dawood in as-Sunan, 198; classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

It was narrated that ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) said: Give each soorah its due of focus of mind and humility. Narrated by Ibn Abi Shaybah in al-Musannaf, 1/324 

Hence Ibn al-Qayyim said:

It was the practice of (the Prophet (blessings and peace of Allah be upon him)) to recite a soorah in full, or sometimes he would recite it over two rak‘ahs, or he would recite the beginning of the soorah. With regard to reciting the last few verses of a soorah, or verses from the middle of it, that was not narrated from him.  

End quote from Zaad al-Ma‘aad, 1/208 

And Allah knows best.