Relation between ADC register value & ADC accessing time?
I don't know any particulars about your specific hardware, but no, the value you read from a A/D should not depend on how long since the last read, assuming the timing specs of the A/D are followed.

If you read a A/D faster than it says you're allowed to in its datasheet, then there is no guarantee what you get.  Often A/Ds actually have two minimum times you must meet, usually called something like acquisition and conversion.

During the acqusition time, the internal signals of the A/D are settling to whatever the input voltage is.  This type of A/D captures a snapshot of the input voltage internally, then does the voltage to number conversion on that.  It can't take this snapshot instantly, hence the minimum acquisition time spec.

The conversion is when the A/D is actively converting the voltage to a number.  This also can't be done instantly.  There are many ways of converting a voltage to a number, with a wide range of conversion times.  However, you don't need to know how the A/D works internally, but you do need to follow whatever rules are spelled out in the datasheet.

If you are violating the minimum acquisition or conversion times, then all kinds of things can happen, including too low a reading.