Reinforcing what others have written:
On many 286/386 computers, the symptom has the well known cause of 'low voltage at the CMOS/RTC chip during the period that the computer is powered off'. Even the IBM AT suffers from the symptom.
When the motherboard is powered on, the motherboard powers the CMOS/RTC chip and oscillator. When the motherboard is powered off, the battery powers the CMOS/RTC chip and oscillator. The oscillator (the thing that 'ticks' the RTC) is more sensitive to low voltage than the CMOS/RTC chip.
Initially, what is noticed is some loss of some time during the period that the computer is off. As the battery voltage drops further, the amount of time loss gets greater. When the voltage drops below a certain point, the RTC does not advance at all when the computer is off.
See the 'Loss of time' section of [
here].
(In later motherboards, the functionalities of CMOS/RTC chip and RTC oscillator are in one of the chipset chips, typically an
82C206.)
It had a soldered in battery, but it's been replaced by a battery holder by the previous owner.
If the 'soldered in battery' was a rechargeable battery, and the previous owner intended for a non-rechargeable battery (e.g. lithium) to go into the battery holder, then in addition to the battery holder, there should have been be a diode added to stop the battery charging circuitry on the motherboard from attempting to charge the non-rechargeable battery. This is discussed in the 'TYPE: Motherboard designed for internal battery only' section of [
here].
That is the 'diode' that others referred to.