Yes they can be damaged. You can have physical damage which can stop them functioning and to a limited extent you can have coding damage as well.
Physically NFC tags usually break when they are flexed or when subject to extreme heat fluctuations. The NFC tags is made of a chip which is solder bonded to an antenna. This antenna is a loop of wire which - on a label - will run on one side of a thin sheet of plastic and then have a 'return' on the other side. These two locations - the bond and the 'crimp' for the return - are the weak link as flexing can cause breakage. Typically once broken the tag will stop working. It's extremely rare for an intermittent failure where the tag will work and then not work etc.
From a coding perspective it is possible to encode/program an NFC tag incorrectly and then lock the tag. If the tags are locked the data cannot be changed so in a sense the tags would then be permanently damaged.
Seritag - 18 Jul 2023
