@JochenT The eviction counter is not really an indication of a problem - it simply means older data will be ejected, but data just put in recently shouldn't be (unless the memory allocated to memcached is really tiny).
In fact, if the server is running for a really long time, and the data being written doesn't use the same keys (it all depends on your plugins and theme code), eventually older data will be evicted, and that's fine in theory most of the time, though that also means that things like transients that are meant to stick around for a long time may disappear before it's time for them to, which would have happened with persistent storage.
The real issue in my case was the number of allowed connections, which on a busy server was simply outpaced by the number of threads connecting to the memcached server.