The first daytime soap opera to have its episodes preserved....
....was possibly "Autumn Affair", an Australian soap opera which aired from 1958 to 1959. It aired for 156 episodes, of which 155 are held by Australia's National Film and Sound Archive.
Other-1970 soaps to have the majority of their episodes preserved include "Peyton Place" (prime-time soap), "Coronation Street", "Dark Shadows" (only 1 episode is missing, and this show has even been released on DVD!) and of course "Days of Our Lives".
Nice that "Dark Shadows" is on DVD....hey, why not put the old episodes of the others online? "Autumn Affair" at least is probably public domain anyway....
Your mother and I aren't fighting. We're having a discussion.