I have had a 16F877A (@4MHz) working in a hot car cab for two months without a reset. That is a plug for the hardware.

Some of the goodies that come with basic block execution of your program (and PULSIN will be one of them) where interrupts will not.
All I can say is search for Darrel Taylor instant interrupts or study Microchip datasheets to do it yourself, (but you'll probably need an example anyway).
The effect a bit like multitasking, your program does not appear to be held up while pulses are being counted.