Yes, blood cells age. Red blood cells (RBCs), in particular, have a finite lifespan.
Red Blood Cell Aging and Senescence
RBC Lifespan
The normal lifespan of red blood cells in adults is approximately 110 to 120 days.
Age-Related Changes
As red blood cells age, they accumulate damage, especially to their membranes. This damage is thought to make them less fit for circulation.
Destruction of Aged RBCs
The mechanisms by which aged RBCs are removed from circulation are not fully understood, but the accumulation of damage leads to their destruction. This age-related death is referred to as senescence.
In summary, red blood cells do age, and this aging process leads to their eventual removal from circulation.