My dad was the exact same way!! He never had it on because he was worried about the battery dying. His was just an old flip-phone type...not a smartphone. The battery could last several days. But he'd bring it with him in case HE needed to call someone, but he didn't leave it on so someone ELSE could call HIM.
My brother got married in 2010 and my dad had been planning to go. He didn't approve, but he was planning to go. The day before, when I talked to him, he was worried about driving directions once he got to Laramie. So I told him, when you get to Laramie, call me, and I'll meet you and we'll lead you where you need to go. So we agreed on that. The day of the wedding, I'm waiting for the call. We get DD's hair done, we get her dress on her, we take pictures, we're all dressed and ready to go, and I still haven't gotten a phone call. I try to call him....he's got his phone turned off. Ceremony starts....ceremony finishes...BBQ in the park....still no dad, so I'm freaking out, thinking he's lying in a ditch somewhere on the side of the road. I'm calling everyone he knows. "Have you heard from my dad?" Nope...isn't he supposed to be at your brother's wedding? Why, yes, he IS supposed to be here, but he's not, and his cell phone isn't on so I don't know WHY. Finally, he calls me and tells me he just couldn't support it so he decided not to come. He didn't think to CALL me and tell me he wasn't coming. I was pretty ticked over that one. Not just hurting my brother all over again, but to let us think he was coming and then worry about him when he didn't show up. Just turn the phone on so people can get in touch with you!!!