In The Great Gatsby, why is Nick's thirtieth birthday so peculiar to him?

What makes Nick's thirtieth birthday specifically peculiar is that he had forgotten it. He only realized that it was his birthday after the confrontation between Jay Gatsby and Tom Buchanan over Daisy had ended. He only became aware of the fact that he had reached this milestone when Tom asked if he wanted to have some whiskey after Daisy had left with Jay on Tom's instruction. He, almost painfully, declares close to the end of chapter 7:

“No . . . I just remembered that to-day’s my birthday.” 

The fact that this important event had slipped his mind also suggests that Nick had been so involved and caught up in the lives and dramas of others, that he had forgotten about the major events in his. He was distracted by the events unfolding around him and in which he had become an essential participant. During this period, he befriended and admired Jay Gatsby, became a guest in the Buchanan household, arranged a meeting between Daisy and Jay, and had grown attached to Jordan Baker. As such, he was both wittingly and unwittingly drawn into the drama which was to unfold.

Nick's perception of turning thirty provides much food for thought. He muses that:

I was thirty. Before me stretched the portentous, menacing road of a new decade.

Nick's observation leads us to believe that he viewed his aging as a dangerous new journey, possibly something that he was not quite ready for yet. He later also observes as he, Jordan and Tom are driving back to the Buchanan house in Tom's car:

Thirty — the promise of a decade of loneliness, a thinning list of single men to know, a thinning brief-case of enthusiasm, thinning hair.

The irony in what Nick thinks is obvious. The word 'promise' usually signifies something good to look forward to, but all Nick sees is misery. He is clearly fearful of an older future and believes that, metaphorically and literally, he is entering a new time frame in which he will lose much: friends, vitality and hair. He paints a sad preconception that is common amongst many people. As they grow older, they are driven to despair, for they believe that old age is a burden. In this regard, we can sympathize with Nick for he is no different to them.

Nick's perception provides a poignant look into how the fear of aging stifles so many and that there is always a hankering to the past. The desire to repeat that which had gone before becomes, as it was with Gatsby, a search for the holy grail - a foolish fantasy, as Nick told him in chapter six:

“I wouldn’t ask too much of her,” I ventured. “You can’t repeat the past.”

“Can’t repeat the past?” he cried incredulously. “Why of course you can!”

He looked around him wildly, as if the past were lurking here in the shadow of his house, just out of reach of his hand.

Perhaps the last line in the novel best sums up Nick's sentiment on the issue:

So we beat on, boats against the current, borne back ceaselessly into the past.