It is strange indeed that there seems no record of Hezekiah having a wife for the first 14 years of his reign. Those years saw remarkable activity: a single-handed (more or less) reformation of the apathetic ecclesia of Judah, institution of Bible Schools, efforts to strengthen the faithful remnant in the apostate Northern Kingdom, and constant travelling around the nation, inspiring and warning against apostasy. When he is told that he must die, Hezekiah's sorrow seems to have been partly because he had no child. Given his new lease of life, he marries the Gentile Hephzibah and has children- who turned out no good. It would have been totally unacceptable for a King to have no wife; it was almost like a King without a crown. It would have stood out so clearly. Yet it seems a reasonable assumption that Hezekiah chose to be a eunuch for the Kingdom's sake. Admittedly, it may be that we are going from one assumption to another, but there is the implication in Is. 56:3-8 that his example inspired others in Israel to make the same commitment. They are comforted by Isaiah: " Neither let the eunuch say, Behold, I am a dry tree. For thus saith the Lord unto the eunuchs that keep my Sabbaths, and choose the things that please me, and take hold (the same Hebrew word is used five times about Hezekiah, 2 Chron. 29:3,34; 31:4; 32:5,7) of my covenant; even unto them will I give in mine house, and within my walls a place and a name better than of sons and daughters: I will give them an everlasting name, that shall not be cut off" (1). Hezekiah had lamented that he would die without a seed (Is. 38:12 Heb.; Is. 53), and so did those who had also become (in their minds?) eunuchs for the sake of the Kingdom. There was that human desire for a seed, a " house" to perpetuate their name. But they are promised a name in God's house (family) in the Kingdom, better than of sons and daughters in this life. This alludes to Ruth 4:15, where Ruth is described as being better than sons to Naomi. In other words, the Ruth: Naomi relationship, featuring as it did a willingness to deny marriage for the sake of the God of Israel, was a type of our relationship with God.
The eunuchs spoken of in Is. 56 seem to have voluntarily chosen it, they are spoken of along with the Gentiles who had voluntarily taken hold of the covenant (another Ruth allusion). Yet it seems that (because of Hezekiah's example?) they too were going back on their devotion; they were having their doubts. They like him in his mid-life crisis wanted to have a physical family, and were regretting that their name would be " cut off" because they had no children to perpetuate them. And Yahweh is comforting them, that their reward in the Kingdom will be to have an eternal name in God's family that will never be cut off. It could be objected that all the believers will have an eternal name in God's house / family. But their name would be " better than of sons and daughters" ; it seems that because the name given us in the Kingdom will be totally personal and related to our own character and experience of human life (Rev. 2:17), the name given to those 'eunuchs' of Isaiah's day will reflect the fact that they denied themselves a physical family in this life. Their pain, their giving, will be recognized eternally, their name / character will be preserved in God's family for ever.
It is possible that Timothy also went through a mid-life crisis in this area, as Hezekiah did. Paul's warning to middle aged Timothy to " flee youthful lusts" (2 Tim. 2:22) was a sure reference back to Joseph fleeing from the advances of Potiphar's wife. The fact that Hezekiah and perhaps Timothy faltered in their devotion to the dedicated single life when they reached middle age does not mean that we should not consider this option. 1 Cor. 7 implies that in our last days, the result of not taking it will be " trouble in the flesh" anyway. One in three (or worse) fall away anyway, married or single.
(1) In its restoration context, it has been suggested that this passage was a comfort to Nehemiah, who appears to have been a (physical) eunuch, and hence barred from entry to the temple which he was devoted to. Hence his words: " Who is there, that being as I am would go into the temple...?" (Neh. 6:11). Isaiah is comforting him and those like him that they would eternally live in the temple.