Here's a solution:
clc
close all
clear all
% ftp://ftp.cdc.noaa.gov/Datasets/cmap/std/precip.mon.mean.nc
filename = ('precip.mon.mean.nc');
info = ncinfo(filename);
unitsTime = info.Variables(3).Attributes(1);
unitsPrep = info.Variables(4).Attributes(3).Value;
validRangePrep = info.Variables(4).Attributes(2).Value;
labelPrep = info.Variables(4).Attributes(1).Value;
time = ncread(filename,'time');
tDatenum = datenum(1800,1,1,time,0,0);
prep = ncread(filename,'precip');
lon = double(ncread(filename,'lon'));
lat = double(ncread(filename,'lat'));
latlim = [18.029167 19.787500 ]; % N to S
lonlim = [101.904167 103.391667]; % W to E
% note there are no longitudes in your limits
% choices are idxLon = 41 lon = 101.2500
% or idxLon = 42 lon = 103.7500
idxLon = 42;
idxLat = find(latlim(1) <= lat & lat <= latlim(2));
from_datenum = datenum(1979,1,1,0,0,0);
to_datenum = datenum(2019,1,11,0,0,0);
idxDatenum = find(from_datenum <= tDatenum & tDatenum <= to_datenum);
myPrepData = squeeze(prep(idxLon,idxLat,idxDatenum));
myPrepDatenum = tDatenum(idxDatenum);
figure('color','white','Position',[70 500 1200 450]);
hold on
box on
xlim([datenum(1978,1,1,0,0,0) datenum(2021,1,1,0,0,0)]);
set(gca,'xtick',datenum(1979:2:2020,1,1,0,0,0));
plot(myPrepDatenum,myPrepData);
datetick(gca,'x','yyyy','keepticks');
ylabel([labelPrep ' [' unitsPrep ']']);
ylim(validRangePrep);
title(['Latitude = ' num2str(lat(idxLat)) ' \circN Longitude = ' ...
num2str(lon(idxLon)) ' \circE']);
It produces this plot:
