As for the advice of Ibn Umar, it's based upon the same Hadith (of the Prophet) that he himself has narrated. It (Ibn Umar's advice) includes a remedy for prolonged, irrational hope. And that if a person happens to reach the evening, he shouldn't wait for or expect to reach the morning. And if he happens to reach the morning, then he shouldn't wait for or expect to make it to the evening. Rather, he should assume that he'll reach his end before that. More than one scholar has explained the concept of Zuhd, or abstention, in the worldly life with this same meaning.
Al-Marwathee said that Abu Abdullah, meaning Iman Ahmad (Ibn Hanbal), was asked, "What is the meaning of having Zuhd in this life?" He replied, "Not prolonging hope too much – he who says when he wakes up, 'I doubt I'll even reach this evening.'" He then said, "And Sufyaan (Ath-Thawree) said likewise." Abu Abdullah was then asked, "How do we get help in not prolonging our hope too much?" He answered, "We don't know; it's only by success exclusively granted by Allah."
As for his (Ibn Umar's) statement: "Take from your health before your sickness, and from your life before your death." Meaning: Take advantage of being capable of doing righteous deeds with what remains of your health before sickness prevents you from doing them, and from your life before death prevents you.
And in another narration: "Surely, oh servant of Allah, you don't even know what your own name will be tomorrow." Meaning: Maybe tomorrow you will be one of the dead, not the living.
A similar meaning of his advice has been reported from the Prophet from a different perspective. In "Sahih al-Bukhari", it's recorded that Ibn Abbas narrated that the Prophet said:
"There are two blessing that many people are deprived of: health and free time." [Bukhari]
Messenger of Allah said to a man while advising him:
And in the "Mustadrak" of Al-Hakim, it's recorded that Ibn Abbas narrated that the Prophet said:
"Take advantage of five things before five other things: from your youth before your old age, your health before your sickness, your wealth before your poverty, your free time before you become occupied, and from your life before your death." [Al-Hakim, vol. 4, hadith no. 306]
The meaning of this is that all these things can delay or prevent someone from doing good things. Some things personally preoccupy the person such as his poverty, richness, sickness, his old age, or his death. Others are more general like the establishment of the Last Hour, the appearance of the Dajjaal, and other disturbing trials as is mentioned in the Hadith:
"Take the initiative to do (good) deeds before trials come like a piece of a dark night (unexpectedly, unnoticeably)." [Sahih Muslim]
After the appearance of some of these more general events, no deeds will be of any benefit as Allah said:
The day some signs of your Lord come, no good will it do a person to believe then if he neither believed before nor earned good (did good deeds) through his faith. [Surah Al-An'am 6:158]
In the two Sahihs (Al-Bukhari and Muslim), Abu Hurairah narrated that the Prophet said:
"The Hour will not be established until the sun rises from the west. When it does rise and the people see it, they will all believe. That's when the faith of a person will not benefit him." [Bukhari]
And in "Sahih Muslim", the Prophet said:
"There are three events that, when they happen, the faith of a person will not benefit him if he didn't believed before or didn't earned good by his faith: the rising of the sun from the west, the Dajjaal, and when the Beast emerges from the earth." [Muslim]
Also in "Sahih Muslim", the Prophet said:
"Whoever repents before the sun rises from the west, Allah will accept his repentance."
Abu Musa narrated that the Prophet said:
"Allah extends his hand during the night to accept the repentance of the sinner of the day, and He extends his hand during the day to accept the repentance of the sinner of the night; this continues until the sun rises from the west." [Muslim 2759]
So, a believer should the initiative in performing righteous deeds before he's overtaken by destiny and prevented from doing them, either because of sickness, death, or by some of these signs reaching him after which no deed will be accepted.
Abu Hazim said, "(Unfortunately), the merchandise of the hereafter is in little demand. It's about to be spent with no one gaining it except a few, not many."
So, if a person's prevented from deeds, nothing remains for him except regret and sorrow. He will wish to return to the previous situation in which he was be able to do good deeds. But wishing at that time won't benefit him at all.
And turn in repentance and in obedience with true faith to your Lord and submit to Him, before the torment comes upon you, then you will not be helped. And follow the best of that which is sent down to you from your Lord (this Quran) before the torment comes on you suddenly while you don't realize it. (This is) so a person doesn't say: "Oh my grief, I was undutiful to Allah and was certainly one of those who mocked (the truth)." Or (unless) he should say: "If only Allah had guided me, I would've been one of the pious and righteous people." Or (unless) he should say when he sees the torment: "If only I had another chance, I'd definitely be one of the good-doers."
[Surah Az-Zumar 39:54-58]
And He says:
Until when death comes to one of them (those who worship other besides Allah), he says: "My Lord, send me back so I can do good in that which I have left behind!" No. It is but a word that he speaks, and behind them is a barrier until the Day when they will be resurrected.
[Surah Al-Muminoon 23:99-100]
And He says:
And spend (in charity) from what We have provided you before death comes to one of you and he says: "My Lord, if only You would give me respite for a little while (to return to the worldly life), then I'd give charity from my wealth and be one of the righteous." And Allah grants respite to no one when his appointed time (death) comes. And Allah is always aware of what you do.
[Surah Al-Munafiqun 63:10-11]
So, since it's like this, it is incumbent for a believer to take advantage of what remains of his life. In explanation of this, some people say, "The remainder of a believer's life is priceless."
Said Ibn Jubayr said, "Each day a believer lives is a treasure."