、。
I probably have periods of half-wakefulness, which is why I feel the day goes by short.
Literal
Probably self [to-には] half-awakened [genitive-の] time [subject-が] exist-and, because-of-that 1-day [object-を] short feel.
Introspective prose on a slightly clinical topic. The written connective form あり (the verb stem of ある used as a て-form equivalent) chains the first clause to the second — a register marker of careful, essayistic writing, equivalent in function to あって. そのため ('because of that,' 'for that reason') is a formal/written causal connector, more buttoned-up than だから. ~を短く感じる ('feel X as short') uses 感じる ('feel, perceive') with a manner adverb (短く, the ~く form of 短い) and an object marked by を — the standard 'perceive X as Y' construction in Japanese.