In Leo Tolstoy's novella, The Death of Ivan Ilyich, time can be very important for some readers, while others may not deem it important at all.
In the opening of the novella, Ivan's coworkers are discussing the recent news of his death. Overshadowed by the news of Ivan's death, conversation moves to the promotions which may/will come because of the opening. Sections two through twelve tell the story of Ivan's life and death.
Here is where one may find the element of time important or not. For those who do think time is important, the excruciating hours, days, and weeks Ivan suffers could be seen by the reader as painful. Each moment which ticks by (especially seen in section twelve where Ivan screams for three days straight) compounds on the moment before. Time is all which is keeping Ivan alive.
On the other hand, some may not find that time is important at all. Instead, they may focus upon disintegrating marriage, the search for promotion, or Ivan's death itself (apart from time).