There are two main problems (at least) with the uSD card on the RPi. First, due to the popularity of the medium, the marketplace has been flooded with counterfeit cards. Pretty much any vendor, reputable or not, sells counterfeit media and I always make a point of testing before my first use with f3 (linux version of h2testw) even if I bought it from Amazon and it came in SanDisk packaging. I also avoid ultra-low prices. Such cards will have only a fraction of the labeled capacity.
The second problem is that if the RPi is shut down during a write cycle, it is possible that the uSD card will refuse to boot after that due to filesystem corruption. The solution here is to reformat the uSD card using the SD Association's free SDFormatter or gparted (linux) or a combination of both in some extreme cases. The card may show up even after running SDFormatter with no partition. In this case, gparted may be able to create a new partition table and then reformat to FAT32.
Another problem which I have yet to encounter, is that SD cards tolerate only a limited number of write cycles and so can wear out over time. I think this only happens in extreme usage cases.
In your case, it is probably one of the first two situations. It is very doubtful that your RPi is damaging the cards due to a malfunction, but do take care to observe a complete shutdown cycle before either removing the card or pulling the power plug. In a terminal, enter
and wait for the 10 green led flashes to end. You can test and/or reformat the uSD card with a card reader that plugs into a USB port...every Pi owner needs one and they are cheap. I would buy another uSD card but try to salvage the old one as above. Stick to reputable vendors who will take the card back if faulty.