Yes, they do. See this long list of failed altcoins.[1]
Minor cryptocurrencies can fail in some unexpected ways.[2] The classic 51% attack has happened in practice to several altcoins.[3] There's also a "burst mining" attack, which can happen automatically - a big mining pool's control system determines that it would be profitable to divert the pool to briefly mining some altcoins and get all the blocks for a while. Then the difficulty goes way up, and the big pool goes off to do something else. Now the difficulty is so high that no blocks get mined at all for a considerable period of time and transactions stall.
[1] https://bitcointalk.org/index.php?topic=588413.0 [2] http://www.ofnumbers.com/2014/06/03/thread-of-the-day-list-o... [3] https://maxminer.files.wordpress.com/2013/06/ftc_51attack.pd...