Measuring pulses, options for accumulate samples after trigger
I gather that you have a signal or way of interrupting (waking up) a CPU. The MSP430 can wake up from a dead sleep (nanoamps) and get up to a full clock rate (say, \$16\:\textrm{MHz}\$) in less than \$1\:\mu\textrm{s}\$. Nothing else I know of can do that.

I'd love to learn of another, though. So if anyone knows of one, please let me know.

They can also be purchased with FRAM, which means very low power operation and can be written to "forever" just like RAM, but with the non-volatile nature of flash. You might want to consider an FRAM version here.



As an added consideration, not necessarily related to the MSP430, you can also consider synchronizing with software in order to "anticipate" when the next pulse will arrive. Then adjust each time based on new info collected to set the next start. Use PID control loop for this. (If this is a periodic signal that can be predicted.) I do this routinely when writing zero-cross software to examine the mains power line. Each recognition of a pulse can be used to improve the prediction for the next one and, if you know an absolute minimum duration a priori, you can use that to make this work well.