This indeed has a source in the sunnah where our Prophet () has promised Bilal the entrance of Jannah due to the fact that he was always performing wudu' once he lost it and prayed two raka'a:
"The Messenger of Allah (ﷺ) awoke in the morning and called for Bilal, then said: 'O Bilal! By what have you preceded me to Paradise? I have not entered Paradise at all, except that I heard your footsteps before me. I entered Paradise last night, and I heard your footsteps before me, and I came upon a square palace having balconies made of gold. So I said: 'Whose palace is this?' They said: 'A man among the Arabs.' So I said: 'I am an Arab, whose palace is this?' They said: 'A man among the Quraish.' So I said: 'I am from the Quraish, whose palace is this?' They said: 'A man from the Ummah of Muhammad (ﷺ).' So I said: 'I am Muhammad, whose palace is this?' They said: ''Umar bin Al-Khattab's.' So Bilal said: 'O Allah's Messenger! I have never called the Adhan except that I prayed two Rak'ah, and I never committed Hadath except that I performed Wudu upon that, and I considered that I owed Allah two Rak'ah.' So the Messenger of Allah (ﷺ) said: 'For those two.'" (Jami' at-Tirmidhi)
This hadith can be backed up to some extent with some narrations from the two sahihs (See in sahih al-Bukhari and sahih Muslim), but they in first place support the good news given to Bilal then supporting our topic of keeping and renewing ablution once one would loose it. But it is more a recommendation to perform wudu' and follow it by two raka'a for the sake of Allah.
But there are ahadith which can lead to the conclusion that keeping in a state of purity is highly recommended, which re quoted in the two sahihs like:
Once I went up the roof of the mosque, along with Abu Huraira. He perform ablution and said, "I heard the Prophet (ﷺ) saying, "On the Day of Resurrection, my followers will be called "Al-Ghurr-ul- Muhajjalun" from the trace of ablution and whoever can increase the area of his radiance should do so (i.e. by performing ablution regularly).' "
(Sahih al-Bukhari, and a slightly different narration in sahih Muslim)
The Messenger of Allah (ﷺ) said: Should I not suggest to you that by which Allah obliterates the sins and elevates the ranks (of a man). They (the hearers) said: Yes, Messenger of Allah. He said: Performing the ablution thoroughly despite odds, tranverside of more paces towards the mosque, and waiting for the next prayer after observing a prayer, and that is mindfulness. (Sahih Muslim)
These two ahadith seem to emphasize on keeping oneself in the state of purity.
The following hadith seems a bit off-topic or too general:
The Messenger of Allah (ﷺ) said: Cleanliness is half of faith and al-Hamdu Liliah (Praise be to Allah) fills the scale, and Subhan Allah (Glory be to Allah) and al-Hamdu Liliah (Praise be to Allah) fill upwhat is between the heavens and the earth, and prayer is a light, and charity is proof (of one's faith) and endurance is a brightness and the Holy Qur'an is a proof on your behalf or against you. All men go out early in the morning and sell themselves, thereby setting themselves free or destroying themselves. (Sahih Muslim)
as cleanliness must not necessarily mean wudu'!
An other indication is the fact that it is highly recommended to perform ablution before going to sleep:
"Whenever you go to bed perform ablution like that for the prayer, lie or your right side and say, ... (Sahih al-Bukhari and sahih Muslim)
and there are many more ahadith on the virtuous of ablution in both sahihs.