Should a gas Aga be left on when not in use?
Looking at the economics angle the Aga is expensive to run. Energy prices in the UK (not sure where you are but most of the Agas I know of are there) are about £.15 per kWh. If an Aga uses 20,000 kWh of energy per year to run, which is a reasonable figure if it's on all day, it would cost £3000 per year. If you modernize it with a schedule to run 8 hours per day, say, it's £1000 per year. Those figures could be less with your model, exact information is hard to find.
If you scheduled it to only heat up for an evening meal then it's probably 4 hours per day, which would be about £500 per year with those energy estimates, which doesn't sound too bad, however that would limit you your flexibility.
A good quality new cooker (i.e. range in the US) costs about the same as 8 hours usage on an Aga for a year, and would be ready when you need it. Used Agas in good condition get around £3000 on Ebay, you could potentially sell it, buy something different and come out cash positive from the deal.
So Agas are expensive to run unless you need the heat from it, if you buy a programmer it can save you money, it's still probably more economical to replace it with something else. It all comes down to whether you like the Aga style of cooking, if you do then spend the money happily, if you don't it'll get snapped up on the used market faster than I wrote this.