My experience with the Pocket 386 is that it has a useless RTC.
1. Entering BIOS setting will reset the clock to 1948
2. Using date/time from the DOS command line will report the time from the last time you set it.
3. Power cycling will leave you back to the last value you set the RTC's time.
4. Glitches, multiple reboots, turning the power button on/off/on really fast can all wipe the CMOS NVRAM and time/date.
I didn't look at the schematics, but I've been in charge of RTC silicon bring-up in another chip (ARM) and this behaves like it has incorrectly powered the wrong rails and possibly violates the power rail sequencing for the RTC. It's retaining the CMOS and RTC but not running the RTC oscillator.
When I run the date/time commands above. This may be showing the timer interrupt counter rather than reading from RTC each time. I don't know DOS 7 internals well enough to say which. But at some point during DOS start up, it had read the RTC correctly.
There's a lot I like about the Pocket 386. And I enjoyed playing games on it. But I think overall I made a mistake in buying it. I also have a v1 Book 8088 and I preferred the larger keyboard of the Book 8088. The display on the Pocket 386 is heads and shoulders above the v1, and it's not even because I'm dealing with CGA. It's sharper and brighter. And the serial/parallel interfaces on the 8088v2 is especially appealing to me, because I think an ESP8266/ESP32 based fake wifi "modem" would be a real treat on this. I could "dial up" to one of the many online BBSes.
I imagine that the RTC issues are fixable with some rewiring with a soldering iron and patch wires. But is it even worth anyone's time to fix it? Should I gut it and try to upgrade my 8088v1's LCD. Sell it on eBay for a whole lot less than what I paid. I don't know it.