I have a Panasonic DMR-EH50 that has of late, no longer records shows programmed for Saturday morning unless its turned on. It records all other shows during the week.
On Saturday morning, if the DVR is off, which is a standby mode, it will not start recording until it is turned on, then it will start recording, even if the show has already started. During the week, it will record all scheduled shows while off (in standby). I tried turning it on early this Saturday morning and then turning it off to see if that would make it start recording, but it didn't.
Once it starts recording a Saturday show, you can turn it off and it will record all the scheduled shows for that Saturday, but unless it gets turned on during a scheduled recording, it won't record anything on Saturday. Whether or not it is turned on on Saturday, it will record all other scheduled shows during the week.
It also doesn't matter if the shows are a timed schedule, that is it will record the selected channel at the scheduled time, regardless of what's on, or if show is scheduled through the TV Guide feature.
When I bought it three years ago, it worked on Saturdays, it's only recently that this has started to happen.