I've gone through a number of HDMI cables now (I do a lot of plugging & unplugging) and I'm of the opinion that the biggest factor is the connection. Specifically, that which is part of the cable and that which is in the component.

In the component, the cable has to fit snugly and there can't be any play. As I swapped cables over time, these often became looser, especially on cheaper components. I suppose that was one huge advantage with DVI - you could screw it in and it would stay put. They make locking HDMI cables too, but you have to have a component that supports the screw-in lock. The weight of the cable is also a problem, with some really cheap players easily being tipped by a heavy cable. Of course, that heavier cable will put strain on the jack over time as well.

On the cable side, I now look for cables that are actually lighter rather than thicker because of the problems mentioned above, but I make sure the connector is very solid. While there are many after-market cables out there, very few are made well, most of them being machine mass-produced with little attention to weak solder points and cheap moldings. Also pay attention to the boots, the reinforced portion where the cable meets the connector. Even expensive hand-made cables don't always come with solid boots. As an example, I acquired some top-of-the-line expensive Monster cables as part of a lot, and while they sound great, they are still built rather badly. Not to knock Monster too much, but for what the previous owner paid for them, they should have been made better.

When I consider the wear & tear that my cables may get, the list of cables I will spend good money on shrinks quickly. There are bad sounding cables and good sounding ones, but IMO, most of the degradation we often attribute to the cable, is actually the result of a poor connection to the component.