It is possible for a cell to make proteins that last for months; hemoglobin in red blood cells is a good example. however, many proteins are not this long-lasting. they may be degraded in days or even hours. why do you think cells make proteins with such short lifetimes if it is possible to make them last longer?

The cells of the body are perfectly capable of making proteins with a life span of many months, still the cells make proteins which are short-lived. On one hand, they make proteins like hemoglobin having a life span of approximately 120 days, and on the other hand, it makes proteins with life span of few days, such as a tumor suppressor protein. The short lived proteins have their own advantage, as they allow the cells to control their function, and amount precisely.