I only shut down when I will be out of town.
Shutting down resets the RAM, among other things,
The occasional restart or shutdown should not reset PRAM. As long as the computer is plugged into the wall, the contents of PRAM are maintained by a tiny trickle current that bypasses the power supply. Been like that for years. If you are unplugging the computer and the internal backup battery ("PRAM" battery) is now dead as a result, date and time plus a few other things maintained in PRAM will reset however.
The internal backup battery only starts working when the computer gets no external power. If you unplug the computer every night, a battery that would normally last several years can see its life drop to months.
Depending on the iMac model, which in this case we don't yet know, replacing the PRAM battery can take minutes to do at home or, with later iMacs, require an expensive trip to the shop for professional service. It behooves you to leave it plugged into the wall at all tiems to avoid a potentially expensive PRAM battery replacement. The batteries are cheap; it's the labor that will get pricey.
"Plugged into the wall" also means not using a power strip, cpower center, or external backup power supply to cut power to the Mac.
Help us determine is you have an iMac with a user-serviceable PRAM battery by doing "About this Mac" from your Apple menu and, in the resulting window, clicking the "More Info..." button. In OS 10.8, that should give you this:
Please tell us what the line I've indicated with the red arrow reads.