A bit cheeky this one, but we had a problem with our gas boiler this morning - it wouldn't start. As we are on British Gas' HomeCare100 scheme, we phoned them up expecting an engineer to come out today (well we are paying £13 a month for this scheme).
We were told that the Ts&Cs pack (that we never received) states that they cannot guarantee same-day call-outs and that we would have to wait until Tuesday morning(!)
Anyway, we happened to mention our 4-year-old son's medical condition (which isn't serious by any means) and suddenly, we were told that an engineer would be with us this afternoon.
Now I'm not suggesting for one minute that you should lie about your kid's medical problems(!) but it might be worth mentioning if you are ever in a similar situation.