Keeping Muscat de Rivesaltes I've had a bottle of Muscat de Rivesaltes on the shelf for a while but opened it last night for cooking. How should I store the remainder, as I'll be using it rather slowly?

It's a very lightly fortified wine, only 15.5%. I'd keep sherry (18%) tightly stoppered and on the shelf for weeks, but  would freeze a strong red if it wasn't going to be used in a few days.

Drinking it up isn't an option as I'm not much of a drinker, especially alone. So should I treat it like a stronger fortified wine, or like normal wine?
Treat it like normal wine, 15% isn't enough alcohol to preserve it. Refrigerated it will be drinkable for up to 2 weeks and you should be able to cook with it for a bit longer than that. I'm not a huge fan of freezing wine, especially if you're going to be thawing and then re-freezing it, although for cooking you can get away with it. 

Incidentally, most sherries do not have a long shelf-life and should be treated the same way.