ISPConfig has no extra specs for memory usage as ispconfig itself does not use much memory, maybe about 20 - 30 MB.
but I figured that 256M should be sufficient for a simple server running a couple of minor sites
That depends on the usage of the sites. 256 is really low and as you see you are getting out of memory errors, so its too low for your current setup. Does your server ahs a swap file or is it a vserver so no swap is allowed?