That sounds like a plausible theory, all though, what you described as a crc is really a checksum. A crc is similar but much more stringent. It is a polynomial with a characteristic divisor. In implementation is it is a bunch of shits and xors. None the less, that does not affect your theory, it works somewhat the same but the crc for target image must be calculated and then compared to the one in the last number of bytes depending on whether it is a crc8, crc16, or crc32. On the other hand the life time of those modules is 10 yr. About 30 yr ago I wrote a lot of 8051 code and designed a bunch of circuits to do all that. Back then 10 yr seemed like a lot of time. I think this scope is a mid nineties as its serial number is B4xxxx which is the later variety.
Anyhow I need to find out how up/download a new image. As I said above, I am getting an ieee 488 and I have an image I found posted. After that I can see if the same thing happens when power is removed, if so the module battery is bad. I would have thought running the SPC would have written a new freshly calculated crc. Seems like a flaw in the design. I always incorporated such features into my designs as I had an original IBM AT which used the original Mot chip the Dallas module was based on. The original design had a circuit bug that caused the battery to go dead regularly and so even though Dallas fixed the bug in the module, I always incorporated a convenient work around as sometime actions of users drained them. In the end the module was just a bad idea as can be seen now. Something custom that becomes obsolete changed out for something standard that will live seemingly forever.