You can never have enough scopes. This beauty was pretty beat up but $30 at a recycler. After a heavy cleaning of the frame, plugins, connectors and a new power cable it came up and everything worked short of the calibration jack which needed an extra heavy cleaning.

http://i11.photobucket.com/albums/a166/ballsandy/CGS_1186.jpg

I fed it a waveform and let it run for a day to see if anything gave out and it was rock solid. Loaded it into a rack and continued to use it for a few more days and then suddenly the image went to the right and I couldn't move it back. It goes about 3/4 to the left if I fiddle with the horizontal positioning control and then starts acting like it's going out of range.

http://i11.photobucket.com/albums/a166/ballsandy/IMG_1851.jpg

If I press the beam finder the waveform snaps back to the center and I can move it completely to the left or right so long as its pressed or if I remove the 11B1 we get one nice dot in the middle as expected. I've cleaned all the connections and I'm not finding any burned components. I'm baffled why it would suddenly do this after working fine during the burn-in but it's obviously something in the 11B1.

That looks similar to the 529 scope that was very popular in TV stations for decades. The shifting is caused by an unbalanced voltage condition on the plates of the horizontal amplifiers.
I would check your horizontal mag control (switch & pot) as dirty contacts will produce that effect. The mag circuit is in the cathodes of the output tubes.
The vertical amplifiers gives trouble too. If you notice the trace shifting and compressing vertically or running out of gain, the tubes should be replaced. There is a retrofit that replaces the output tubes with transistors. Was published in Broadcast Engineering magazine back in the seventies. You can probably find the mod online.
Good luck.

Unfortunately this model is solid state so the only tube is the CRT. ;)
That said, that does put the option of a failed transistor on the table.

If you don't have a service manual for the R647a you can find it at the bama site,bama(dot)edebris(dot)com/manuals/tek/647a/. All the best, Tom

A manual/schematic is available online at:

http://w140.com/tekwiki/wiki/11B1

It sounds like something is upsetting the horizontal amp stages. If it only happens after running in a rack for a while, suspect a transistor with internal leakage. A can of freeze mist should help localize it.