Welcome to NICO Club!
Tell us exactly what happens when the car dies. Temp gauge rises, power flickers, engine sputters a bit or just dies, etc. Also, what happens when you try to start it right after it died. Like if it turns over ("cranks") but won't fire, or fires, but won't run, etc.
Off the top of my head, you have an electrical problem at a critical point and it's loosing the connection, therefor shutting off your engine. Something get's wiggled on the tow home and all is fine when you try again later. That would explain why you aren't getting codes, because the ECU has no power and therefor can't store the codes. Another thought is heat causing a cut out and it won't start until cooled, but I'm not leaning towards that as much.
Check the battery and all your ground connections. Here is a link to the FSM for help with diagnoses:
http://www.nicoclub.com/FSM/Altima/2001/
Maybe look into the stuff in the EC chapter, starting at page EC-91. There's a chart there and stuff to look at for a hard start/ no start/ restart condition.