Sometimes it works immediately, and other times it comes on in the middle of the night even though I switched it on in the evening (it doesn't go off though, so it doesn't seem to be a loose connection problem).
Thanks very much for your help!

Has the light switch ever been replaced since this started?

Is it a fluorescent?

To tommybwiz - yes, the bulb is fluorescent
To smoothly - I'm not 100% sure, but I'm fairly sure it hasn't been replaced since the house was first built

Have the switch replaced.

If this is a "tube type" fluorescent, try changing the bulbs. Are there blackened ends on the tubes? Also, another issue if this is tube type,would be either the ballast, if it that type, or starter. Fluorescents can be funny. Sometimes its nothing more than a bulb that needs to be twisted a little more. I've also seen T-8's installed in T-12 fixtures cause a problem.