ooops, wrong circuit at the previous post... I am getting old and dumb,
this one here doesn't need even the resistor to keep PIC +V polarized
and hold /CE /OC and /W at up level while switched off. The Ram chip
will be at 0.7V above ground when PIC is energized, I can't see any
problems, do you?

+5VCC--------o---------------o--------------.
             |               |              |
             |               |              +
            PIC             RAM             3V
             |               |            Backup
             |               |            Battery
    Switch   |               |              |
        /    |    diode 1    |    diode 2   |
Gnd---o/ o---o------|<-------o------>|------'