The Uno is a 5V device. So its Voh is close to 5V. The MRFC522 is a 3.3V device. Its maximum Vih is 3.8V. Connecting the Uno's outputs directly to the MRFC522's inputs will eventually damage the MRFC522. Sometimes you get unlucky on the very first time out, and that may very well be what has happened to you.
I'm aware that there are many places on the web that say "oh, it's perfectly safe to do this", but I tend to believe the datasheet when it says that 0.5V over the supply voltage, or 3.8V, is the limit. But don't take my word for it: feel free to peruse the datasheet yourself and come to your own conclusions.
To safely operate the MFRC522 with a 5V board, at a minimum you need voltage dividers on SCK, MOSI and RST to bring the high level signal down to 3.3V. I prefer to use active level conversion. You can do that with little more than a 74AHC125. The wiring isn't onerous. I also prefer to use a discrete 3.3V regulator rather than rely on the limited current capacity of the 3.3V output on some Uno clones.
