Mindfully they give up wrong view and take up right view: that’s their right mindfulness.
So sato micchādiṭṭhiṃ pajahati, sato sammādiṭṭhiṃ upasampajja viharati, sāssa hoti sammāsati (MN 117)
According to above passage, one would argue that the mind of an arahant cannot give up the right view and therefore he is always mindful. Further the mindfulness of an arahant is automatic because an arahant can never take up wrong view since the arahants already developed all 8 limbs of the Noble Eightfold Path to perfection such that they’ve become second nature.
MN 104 says sativinaya should be given to a bhikku who don’t recall the offense when they are accused to a defeat or some act close to a defeat; explained in Samathakkhandhaka. This is for arahants, to keep them safe from being accused again. sativinayo
Explainations in the Sukkavisatti rule also says that those who go to sleep mindfully does not undergo wet dreaming and it also says arahants never ejaculate semen. This may be due to their mindfulness?
Eventhough this is doubtful, the blessed one seems always mindful. DN 16 appears to say that the Buddha endured his physical pains mindfully (satova).
After the Buddha had commenced the rainy season residence, he fell severely ill, struck by dreadful pains, close to death.
Atha kho bhagavato vassūpagatassa kharo ābādho uppajji, bāḷhā vedanā vattanti māraṇantikā.
But he endured with mindfulness and situational awareness, without worrying.
Tā sudaṃ bhagavā sato sampajāno adhivāsesi avihaññamāno. (DN 16)
Before drawn into a conclusion, there are a set of suttas to consider.
1. Tatiyagilāna Sutta SN 46.16
When the Buddha was sick, Mahācunda taught him the awakening factors, inspiring him to a swift recovery.
2. Dutiyagilāna Sutta SN 46.15
When Mahāmoggallāna was sick, the Buddha taught him the awakening factors, inspiring him to a swift recovery.
3. Paṭhamagilāna Sutta SN 46.14
These suttas show some stuaions where reminding bojjhaṅgas helped healing sickness.
If they are able to be mindful how reminding bojjhaṅgas help recovering from sikness?
However, is it possible to always be mindful or they are mindful only when they take it up?