I have had the same problem with several HP-25's which I bought in unknown working condition. Some were like that from the start, another was like that after I got it to work at all. Finally I bought one from a collector that was known working. When I received it, I found its memory was a little flaky, I would enter a program and sometimes it would change a little. I discovered that the capacitor in the clock circuit had been changed, apparently to speed up the calculator. I can't remember whether I figured this out by comparing the component values on the several units I had by then, or if I measured the frequency and found it different from another unit or from something I read in the Museum, but I remember that when I found the difference, it was obvious that the capacitor had been changed. When I put the correct capacitor value in, the memory became stable. Also, along the way I figured out which chip was the RAM chip by brute force - from one of my bad-memory units, I removed chips one at a time till I found one that made no difference! Later I read the Museum Technology article for Woodstocks which explains how the functions are divided among the different chips. While I don't have my notes in hand, my memory (also somewhat flaky!) says that if you hold the circuit board component side up with the place where the keyboard attaches at the bottom (same orientation as if you were using the calculator), the RAM chip is the vertically oriented 18 pin chip (0.3 inch wide) to the left of the larger, horizontally oriented 22 pin chip (0.4 inch wide) which is the CPU (I think it is called the ACT). On my newest working unit, the part number of the RAM chip is 1818-0154. Also on this unit, the clock components, which are the capacitor and inductor connected in parallel and to pins 13 and 14 of the 22 pin chip, are a 330 pf capacitor (marked "331") and an inductor with the following bands (I've never learned how to read inductors properly): wide silver, brown, green, brown, narrow silver. (I guess that's actually a pallindrome.) My recollection is that the wide first band signifies an inductor (rather than a resistor) but I thought the first band was one of the significant digits, and silver can't be a significant digit, it can mean 10^-2 multiplier or 10% tolerance. The other bands, if it were a 5% or 10% resistor, would mean 150 ohms, so maybe this is a 150 microhenry inductor. 150 microhenries and 330 picofarads would have a resonant frequency of about 715 kHz, which sounds about right.
Because I found several units with this problem, I thought it might be a well-known problem and I have asked in this Forum if others have had the same problem, but I've never heard from anyone who has found this to be the case. There was a recent thread about another Woodstock that has a frequent failure and there is an article in the Museum Articles page about it, but I believe in that case it is a chip specific to that model that fails.
It is my understanding that several of the Woodstocks use the same RAM chip, I suppose any model with 8 data memories and 49 program steps would. The 25 is the only Woodstock I have, although I think I now have six of them (2 completely working).
The problem is, you have to find another calculator to take the chip out of, but unless that calculator is working substantially completely, how do you know if the memory chip is working? If you were lucky enough to find another 25 that worked except for a bad display digit or a bad keyboard, then you could replace your main circuit board with the one you found, this is very easy as the modules plug together.
One theory, at least, of why the memory chip goes out while the rest of the calculator is working, has to do with the weakness in the way HP designed the battery charging circuit. If the connections between the NiCad cells and the calculator develop a high resistance (such as when the cells leak and corrosion occurs), the voltage from the charging circuit at the calculator battery terminals, which is the power source for the calculator, rises to a higher voltage than normal. In other words, HP designed the battery circuit with the NiCad cells providing voltage regulation as well as power storage. The 2.5 volts from the battery is converted to +6 volts and -12 volts for the MOS chips (when the calculator is on), so when the battery voltage rises, the converted voltages rise proportionally. One thory is that the design of the RAM chip makes it more sensitive to a higher supply voltage, so it fails first.