I can set a reminder on my iphone using SIRI or manual entry and it works as expected. Wife has exact same phone/IOS but reminders don't work, here's what happens. A reminder is set, then the date/time is set, press Done. I see the reminder I just set, with the date/time just below it. After 2 seconds, the date/time disappear. Go into details for the reminder and date/time is blank. Set it again, back to list and see the date/time...2 seconds later they disappear as you watch it. With no date/time, the reminder obviously doesn't work. Reminders are allowed in Notifications. I upgraded her IOS last night so her phone has been restarted.
I don't have her phone with me, so I can't try anything right now. But, if anyone has seen this or has ideas, I welcome them.