So is there a button or something, to just turn off the LCD screen, and it turns off, but then keeps turning back on ?
On all the LCD stuff I worked on lately, there was an MCU with outputs specifically meant for directly driving LCD segments/com's. And only that MCU had final control over output to the LCD. However on the DMM I was working on, there was another MCU, telling the LCD MCU, what to do.
There could be some external logic gate circuit getting mixed up, and turning the LCD back on. I'd want to know where the signals to the LCD come from, what IC, and what other IC's is it connected to ??
Why do you think it's power related ? Have you checked it already with a DMM and know it's related ? Maybe there's a backlight, does it also come back on ?? Maybe the whole unit is powered off to disable it, and power gets sent back to it when it's not supposed to be. If it was something like that, yeah I'd be looking at any enable pins and logic circuits for enable signals.