I missed a show last week and was lucky to find it on ROD. Got about 10 minutes into and then had to do something, so I saved it to finish the next day.
Next day I start to watch it and as soon as I get to the point where it's been 24 hours since I started watching the day before the show stops. I am about 35 minutes into the 1 hour show and the only option is to start again. This wouldn't be much of a problem, except fast forwarding is disabled and you have to watch the whole thing again to get to the point of you were before.
It you are watching the show, it should let you finish, even if you are beyond the 24 mark!!