What is the idiom or expression to describe the state that a person interrupts their happy time by believing that “this will end soon “?

There are some people who don't enjoy the available good time and sometimes it even worries them. I am not sure why, but they might think that they will miss those moment and suffer for the lack of it.

One U.S. idiom for a person who constantly frets even when nothing is seriously wrong is worrywart. Here is the entry for that word in Barbara Kipfer & Robert Chapman, Dictionary of American Slang, fourth edition (2007):

worrywart n phr A person who worries excessively; a constantly apprehensive person {1956+; fr the designation of such a person in the comic strip "Out Our Way" by J R Williams}

Rosalind Fergusson, The Facts on File Dictionary of Proverbs (1983) has a relevant saying about people who can't relax and enjoy a pleasant situation:

He that has no ill fortune, is troubled with good. [The implication is that certain people will always find something to worry about]

The bracketed comments in the two quotations above appear in the original texts.

Charles Doyle, Wolfgang Mieder, and Fred Shapiro, The Dictionary of Modern Proverbs (2012) has two sayings that address the senselessness of endless worrying:

Worry is interest paid on trouble before it is due.

(which the dictionary traces to a collection of sayings from 1909) and

Worry is like a rocking chair: it gives you something to do but doesn't get you anywhere.

(which it dates to 1916).

The state in which a worrywart is most comfortable (or uncomfortable) is sometimes termed worrywartism. From David Sue & Stanley Sue, Abnormal Behavior (1990) [combined snippets]:

Social phobics are frightened only of a specific activity performed in public; generalized anxiety disorder involves chronic "worrywartism."

So to describe the state of a person who can't fully enjoy a happy time because "this too shall pass," you could use the (somewhat unusual) idiomatic term "worrywartism" or the (somewhat specialized) clinical term "generalized anxiety disorder."

anhedonia is a psychological condition characterized by inability to experience pleasure in normally pleasurable acts. Merriam-Webster

Inability to feel pleasure in normally pleasurable activities OED

from Wikipedia

• Anhedonia is defined as the inability to experience pleasure from activities usually found enjoyable, e.g. exercise, hobbies, music, sexual activities or social interactions. It is a characteristic of mental disorders including mood disorders, schizoaffective disorder, borderline personality disorder, schizoid personality disorder and schizophrenia.

Someone fears that something is too good to last.