Well I'm not a clothes expert, but I do have some idea as to how washing affects the wear of clothes.
Washing clothes is sort of a double edged sword. On the one hand, it removes dirt, dust, and other abrasive material that speeds the rate at which the garment breaks down. In addition, unwashed clothes harbor bacteria or other microbes which, at least on natural materials such as cotton or my fortresses famous xhemp plant fiber mittensx, will cause the material to break down as well, albeit slowly.
On the other hand, as already mentioned, washing a piece of clothing causes wear itself, mainly through the scrubbing process, so washing clothing isn't entirely without its negatives.
Perhaps a hybrid form of the "resetting the degrading time" idea would be in order. For instance, when washed, the degrading timer for that piece of clothing could be reset, but the time until degrading could be reduced by some fixed or random amount. For instance, sock A has 3 months left before it degrades to xsock Ax, and had a total time of 8 months before it was degraded when it was first made. Sock A is washed and the timer is reset, except this time there are only 5.8 months of time before it becomes xsock Ax. In this way, no piece of clothing would last forever, but washing would have a tremendous affect on the overall durability of clothing.