My 2000 did essentially the same thing, cut out and would start right up again -- at least until the time it DIDN'T start again. Wouldn't throw a code, either. Came in on the hook.
Mech. replaced the crankshaft position sensor and it seems (SEEMS -- it's only a week) to be OK.
You might also check the fuel-pump relay; in mine anyway, the relays all are the same, so you could swap the horn relay with the fuel-pump relay. New one is less than $15 in any case. BTW, they're a PITA to get out -- you may need to grab the relay GENTLY with a pair of pliers and GENTLY rock it back=and-forth while lifting.