Thu Feb 27, 2014 12:40 pm
Hiu and welcome to the forum.
That is expected operation. The LCD is dumb - it only displays what it is told to do. Also it does not have a reset line, so it does not know that the Pi has been reset unless the software controlling what is displayed tell it to display something else or CLS, for example.
Hope this helps,
Texy
Various male/female 40- and 26-way GPIO header for sale here ( IDEAL FOR YOUR PiZero ):
https://www.raspberrypi.org/forums/viewtopic.php?f=93&t=147682#p971555