I’ve noticed, ever since I put battery power to Harlem again, that her clock for some reason seems to now lose about 2-3 hours over a day or two period. 
She always kept accurate time before her “hibernation” and even now her ticking seems to be at about the correct rate (at least to my ear). 
Anyone have any idea what’s wrong, or whether the time “speed” is adjustable somehow on the clocks? 
Anyone have any ideas on this ?
Its a clock. Take it to a clock repair shop. I think the clock gets power and that’s about it.
If you’re concerned about whether its getting enough power, you’d have to take a reading using a multimeter, then compare the reading you get with what the electrical diagram shows you…maybe 5v, maybe 12v, maybe something else?
If you find the voltage supply, you can test it by plugging it into a temporary power source. Batteries here would do just fine. You can find out if it’s loses time when attached to the alternate source. If it does, you know there’s a problem with the clock.
They shouldn’t be that expensive to replace. You might be able to find one on eBay for a lot less time and money that you would spend trying to figure out the problem.
That’s what I was thinking, VK … Saw one on Ebay for only $25 or so … They appear to r/r easily, too … 
The x300 series clocks are noted for failure, here’s a previous thread with a six dollar fix I used and am quite happy with.
Thanks, Bob … Unfortunately, when you click on that (Ebay) page it shows it “no longer exists”. Oh well, I guess I’ll just get another one … As VK pointed out, there are used ones available on Ebay, and one of my usual suspects has one for sale for only $25.00. 
A rebuilt may be a better choice for longevity, but carful of the surgery
in the dash at any rate. Less than $6 delivered, I used mounting putty,
looks factory, batteries go about a year.
Not bad, and it looks like it even tells temp in the car. I usually buy a lot of stuff on Ebay for my Jags, but am starting to get a little wary, esp. of those vendors in China. I bought a hot glue gun last week (to use with a dent-puller gizmo), and in their ad they show like 4 different attachment heads for power, one of which is for plugging into the cig lighter. This is the main feature I wanted, so I went ahead and bought it. Item arrives and all it works with is standard 120 a.c. . I was not happy, and at first the vendor seemed to be calling me stupid for not realizing it was only made for 120. 
I pointed out his picture showing the four power heads, and that at best it was confusing. He seems to be “resisting” giving me a refund, but I’ll keep pushing for it. 
Product not as advertised or presented usually does it with ebay to get a refund, they tend to favor the buyers side, but make sure you are within their assigned time limits for filing a claim. My cheapo clock is 3 yrs going fine, temp in in C only.