Is the frequency stable and guaranteed 2kHz +/- (margin proportional to the duty cycle threshold margin)?
If so, a missing pulse detector is a fine solution. It's also the fastest possible solution (latency of ~1 cycle on average).
If not, an LPF + comparator is pretty good, minding that the LPF needs to roll off considerably lower than whatever the true minimum frequency is. This of course isn't a problem over the requested duration (sub 1 hour).
Don't forget hysteresis on the comparator, to prevent false triggers from the LPF's leftover ripple when it's borderline near the threshold.
You will want to use an active filter, to keep component size and cost down. Although if the 220k + 4.7uF shown above is acceptable, that's not too bad. Try to avoid using electrolytic capacitors here. Film caps are very large, but good. Tantalum is actually quite reasonable (okay leakage, stable value, no danger of shorting out a supply!).
If very low supply consumption is desirable, you can choose some nice slow CMOS op-amps and comparators. A comparator with response time in the 5us range sips little enough current that it can run from a battery for months, maybe even years on end. They perform quite well, when you don't need screaming speed.
Tim