Apennines mass is a constant set fourth by the minting agency that puts out the coin. If the penny is handled however making many cycles through circulation it may be worn slightly thus decreasing its mass a little, however the amount of wear might be negated due to the fact that in circulation the penny is exposed to outside air and numerous contaminates from fingers, pockets, drawers etc. Which would increase the pennies mass slightly with tarnish deposits and what not. I would say that pretty much, except for isolated incidents, the penny will weigh the same, the weight being the measurement of the gravitation pull on an objects mass. If the weight stays the same then the mass by default must be the same, if you are on earth where the gravitational pull to earth inside the atmosphere is a constant.
Pennies will not be affected by ageing as long as there will be nobody that will interfere or made contact with this penny that will change its chemical composition.