Monostable Multivibrator One Shot - action with input held indefinitely
How about a 555 timer as a monostable multivibrator? It is cheap, simple to use and available about everywhere. Do check the paragraphs on "Trigger pulses", which either triggers the circuit once or keeps leaves the output active in case the input pulse is of longer duration than the output mono time.

Or check out 7555 for a less power hungry CMOS variation of the chip.