The problem: you have a great scope but it doesn't hold calibration when you turn it off. The source of the problem is the Dallas NVRAM chip from the late 80's has finally run it's battery down. The solution: replace that dead chip with a new Maxim chip.

If you see the errors from the photo here when you turn on and run selftest, but they all pass if you rerun after the self calibration, this should fix your problem.

Step 1: Parts and Tools

There are very few necessary tools and fewer parts.
Tools

Torx 10 bit
5/8inch wrench
soldering iron
solder sucker
optional: desoldering iron (cheap RadioShack one does the job)

Parts

Maxim Integrated DS1230Y-120+ (approx $30, but available as a sample from Maxim)
28 pin IC socket, mouser #575-199628 works great (not necessary but highly recommended)

Step 2: Remove the Cover

Safety first: Unplug the unit.
Remove the cover, there are 6 screws on top and 2 on each side.

You will be greeted by a nice warning against touching things and a nice view of the beautiful through-hole construction.

Remove the power supply: Do not remove any of the power supply screws, they're not necessary to this step. Remove the two high tech power supply retention pins (two white things that look like styluses), disconnect the ribbon cable and mains connector, the power supply then just slides out.

Step 3: Remove the Back Cover

Remove the 8 screws from the back panel and pull it off carefully, it will stick in the bottom left corner until the pin inside unseats from its socket.

Disconnect the three connectors to the main board, feed the mains connector through it's hole in the chassis and set the back cover aside.

Step 4: Remove the Main Board

Flip the scope on its side and remove the 8 screws on the bottom. Then remove the nuts on the 4 input connectors on the front.

Next disconnect the fan's power connector, the ribbon cable that connects to the side board, and the power extension ribbon cable.

The main board should now slide out the back smoothly.

Step 5: Replace the Chip

The chip in question is marked U37, it's a Dallas DS1235YW.

Flip the board over and locate the opposite side of the chip. Remove the chip by desoldering each of the 14 pins, there are many guides on doing so, just be patient and don't force it. If you pry at the chip you'll scratch the board.

I added a socket when I replaced my chips, to make any future replacements easier and to prevent possible damage to the chip. Pay attention to which direction pin 1 goes.

Put the new chip in the socket, paying attention to pin 1 orientation.

Step 6: Put the Whole Thing Back Together

Slide the board back into the chassis.
Put the nuts back on the input connectors and put the 8 screws back into the bottom of the unit to hold the main board in. Reattach the fan power connector and the side board connector. Connect one end of the power supply cable.
Reattach the back panel, reconnect the three cables and then the pin on the bottom left seats into a connector on the main board.
Slide the power supply back in and reconnect the ribbon cable and mains connector.
Put the top cover and its 10 screws back in place.

Step 7: Power Up and Calibrate

Set the calibration switch on the back to unprotected then power on the unit while holding a key in on the front panel. The scope should alert you that the default calibration has been loaded.
Now you can go through the self calibration process, which you may be familiar with, if not follow along.

Press the Util button, go to the Self Cal menu. Select cal 0, channel 1 (both are the default selections), then press Start cal. The scope will remind you to connect a cable from the DC port on the back to the channel 1 input, then press continue. After several minutes the calibration will succeed, change to cal select 1, swap the cable from DC to the AC port and press continue. The delay cal goes much quicker.

Repeat this process for each channel and you're done.

The calibration will now be saved through powering off and back on, no more recalibration.
Move the switch on the back to the protected position to prevent overwriting the calibration.