I have problems going back and forth with the num2date and date2num routines.

One problem is a millisecond problem:

import cftime as cf
import datetime as dt
dt1 = dt.datetime(1810, 4, 24, 16, 15, 10)
cf.num2date(cf.date2num(dt1, units='days since -4713-01-01 12:00'), units='days since -4713-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 9, 999999)
cf.num2date(cf.date2num(dt1, units='days since 0001-01-01 12:00'), units='days since 0001-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 9, 999999)
cf.num2date(cf.date2num(dt1, units='days since 1600-01-01 12:00'), units='days since 1600-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 9, 999999)
cf.num2date(cf.date2num(dt1, units='days since 1700-01-01 12:00'), units='days since 1700-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 10, 0)

The other one is off by one week if I use Lotus dates (or Excel 1904 dates):

dt2 = dt.datetime(1271, 3, 18, 19, 41, 34)
cf.num2date(cf.date2num(dt2, units='days since 1904-01-01 00:00'), units='days since 1904-01-01 00:00')
-> Out: cftime.DatetimeGregorian(1271, 3, 11, 19, 41, 34, 0)

I am the one who did the pull request once: Unidata/netcdf4-python#433, adding a little offset corresponding to about 45 milliseconds. So I if do the same here, I get the right seconds but not the right microseconds, of course:

import numpy as np
eps = np.finfo(np.float).eps
dt1 = dt.datetime(1810, 4, 24, 16, 15, 10)
j1 = cf.date2num(dt1, units='days since 0001-01-01 12:00')
cf.num2date(j1, units='days since 0001-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 9, 999999)
j1 += np.abs(j1) * eps
cf.num2date(j1, units='days since 0001-01-01 12:00')
-> Out: cftime.DatetimeGregorian(1810, 4, 24, 16, 15, 10, 9)

Perhaps you could introduce the rounding of microseconds again, just as you did for issue #78.
I have no idea about the missing week though.

I use cftime version 1.2.0 on Python 3.8.3 on macOS 10.15.5.

Kind regards
Matthias