Is it recommended to do the Sunnah prayers all the time, or is it better not to do them sometimes so that they do not become like the obligatory prayers?

Firstly: 

Always doing that which Allah has made obligatory is one of the duties of Islam, and is the foundation of steadfastness on the straight path of Allah. Always doing the regular Sunnah prayers in particular, and virtuous deeds in general, is something that is recommended in Islamic teaching. The Prophet (blessings and peace of Allah be upon him) was asked: Which deed is dearest to Allah? He said: “That which is done persistently, even if it is little.” Narrated by al-Bukhaari (6465) and Muslim (782).

 Al-Bukhaari (1987) and Muslim (783) narrated from ‘Alqamah: I said to ‘Aa’ishah (may Allah be pleased with her): Did the Messenger of Allah (blessings and peace of Allah be upon him) single out any particular day for anything? She said: No, his actions were persistent, and who of you can do what the Messenger of Allah (blessings and peace of Allah be upon him) could do? 

An-Nawawi (may Allah have mercy on him) said: 

The words “his actions were persistent” mean that he would always do them and not cease to do them. 

Al-Haafiz (may Allah have mercy on him) said:

 The linguists said that the word daymah (translated above as persistent) originally referred to rain that lasts for several days, then the word came to be used to refer to anything that is ongoing. 

Al-Bukhaari (6461) and Muslim (741) narrated that Masrooq said: I asked ‘Aa’ishah (may Allah be pleased with her): which deed was most beloved to the Prophet (blessings and peace of Allah be upon him)? She said: That which is done persistently. 

Muslim (746) narrated that ‘Aa’ishah said: If the Messenger of Allah (blessings and peace of Allah be upon him) did an action, he would persist in it. If he slept at night or was sick, he would still pray twelve rak‘ahs during the day. 

Thus it is clear that there is nothing wrong with persistently doing Sunnah and naafil righteous deeds, in fact that is recommended and encouraged, because that was what the Prophet (blessings and peace of Allah be upon him) did and taught others to do, and he encouraged others to do that in more than one hadith, such as that which was narrated by at-Tirmidhi (414) from ‘Aa’ishah (may Allah be pleased with her), according to which the Prophet (blessings and peace of Allah be upon him) said: “Whoever persists in praying twelve rak‘ahs of Sunnah prayer, Allah will build for him a house in Paradise.” Classed as saheeh by Shaykh al-Albaani in Saheeh at-Tirmidhi. 

Abu Dawood (1269) and at-Tirmidhi (428) narrated that Umm Habeebah, the wife of the Prophet (blessings and peace of Allah be upon him) said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Whoever persists in praying four rak‘ahs before Zuhr and four rak‘ahs after it, Allah will forbid him to the Fire.”

Classed as saheeh aby al-Albaani in Saheeh Abi Dawood. 

At-Tirmidhi (3410) narrated – and classed it as saheeh – that ‘Abdullah ibn ‘Amr (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “There are two deeds that no Muslim man persists in doing but he will enter Paradise. Indeed they are easy but those who do them are few: glorifying Allah (by saying Subhaan Allah) following every prayer ten times, praising Him (by saying al-hamdu Lillah) ten times, and magnifying Him (by saying Allahu akbar) ten times. That is one hundred and fifty on the lips and one thousand and five hundred in the balance. And when you go to bed, then glorify Him, magnify Him and praise Him one hundred times; that will be one hundred on the lips and one thousand in the balance. And who among you could do in one day and night two thousand and five hundred bad deeds?” They said: How could anyone fail to do that? He said: “The Shaytaan comes to one of you when he is praying and says: Remember such and such, remember such and such, so that when he finishes his prayer, he may forget to do that; or he comes to him when he is in his bed and keeps on making him sleepy until he falls asleep. 

It was also narrated by Abu Dawood (5065) as follows: “There are two deeds that a Muslim does not do regularly but he will enter Paradise. They are easy but those who do them are few…

Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.                     

Al-Mubaarakfoori said in Tuhfat al-Ahwadhi: 

“Those who do them are few” i.e., those who do them consistently. 

Secondly: 

With regard to them not being like the obligatory prayers, this is clear, and it is sufficient for the individual to be aware of that and to intend them as naafil whilst doing them, and make that clear to people, if he is explaining the Sunnah to people. We are not now living at a time in which the teachings of Islam were fresh and new, where it can be imagined that people could confuse obligatory deeds with naafil ones.

Moreover, it will inevitably happen that a person may be interrupted by urgent work, travel, sickness and the like. In such cases there will be stored up for him that deed that he stopped doing, and he should not deliberately omit it because of what is mentioned above. 

Thirdly: 

With regard to that which it is narrated in the Sunnah that the Prophet (blessings and peace of Allah be upon him) did it sometimes and did not do it sometimes, if this is how it was done by the Prophet (blessings and peace of Allah be upon him), one should pay attention to that by doing that thing sometimes and not doing it sometimes, because that is preferable to doing it constantly.

 An example of that is sometimes reciting in the last two rak‘ahs of Zuhr and ‘Asr prayer something in addition to al-Faatihah, and so on. 

And Allah knows best.