The Alpha Clock Five schematic essentially arranges the full set of LEDs on the segmented displays as a rectangular matrix with 5 rows (one for each segmented display) and 18 columns (one for each segment in the display).
The columns are switched by two LED driver chips, U2 and U3, and the rows are switched by drive transistors Q1-Q5.
If all of the LEDs are lighting (even in one display) when they should, that suggests that the LED driver chips (the columns) are likely operating properly.
If not all of the segmented displays are lighting, that suggests strongly that something is going on with the row drivers. The signals to control those transistors originate at pins 36-40 of the microcontroller (U1). Those signals go through U5, which essentially acts as a level shifter, before going to RP6, a set of resistors that are connected to the transistors.
Since you’re seeing what appear to be *multiple* digits failing, the most likely cause is that something is flaky with U5. I’d start by checking that the chip is securely seated, and then check it solder connections. Next up would be to check soldering at RP6, and to begin checking the connections from U5 and RP6 to the microcontroller.