A sensor samples and transmits status updates to a destination through a wireless channel that wears out over time and with every use. At each time slot, the sensor can decide to sample and transmit a fresh status update, restore the initial quality of the channel, or remain silent. The actions impose different costs on the operation of the system, and we study the problem of optimally selecting the actions at the transmitter so as to maximize the freshness of the information at the receiver, while minimizing the communication cost. Freshness is measured by the age of information (AoI). The problem is addressed using dynamic programming, and numerical results are presented to provide insights into the optimal transmission policy.