Your pic shows the main fuel (PGM-FI) relay. It's supposed to click on startup, around the time the fuel pump primes. Normally (at least in my experience) it's not loud enough that you'd notice it unless you're putting your ear close to it or, perhaps, if you try to crank the car and nothing happens.
Maybe it was getting power sporadically and so was clicking off and on over and over again, causing you to notice it. If that were the case, I'd again lean towards a connection issue at the battery or perhaps the ignition switch.

Since I'm not hearing the clicking the main relay is making, it's hard for me to say whether what it's doing is normal, but it is normal for it to click. In fact that's an indication that it's working correctly. If that relay was preventing the car from starting and/or causing it to die (as a result of no fuel flow from injectors), you'd expect the relay to click fewer times than normal or not at all.

Btw, when you say it died, did it start for a second and then die, or were you actually driving it when it died?