BUG: `pandas.DataFrame.plot` results in inconsistent/incompatible `xticks` depending on the date span of the data

[X] I have checked that this issue has not already been reported.
[X] I have confirmed this bug exists on the latest version of pandas.
[ ] I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# sample data
dates1 = ['2021-08-26', '2021-08-27', '2021-08-30', '2021-08-31',
          '2021-09-01', '2021-09-02', '2021-09-03', '2021-09-07',
          '2021-09-08', '2021-09-09', '2021-09-10', '2021-09-13',
          '2021-09-14', '2021-09-15', '2021-09-16', '2021-09-17',
          '2021-09-20', '2021-09-21', '2021-09-22', '2021-09-23',
          '2021-09-24', '2021-09-27', '2021-09-28', '2021-09-29',
          '2021-09-30', '2021-10-01', '2021-10-04', '2021-10-05',
          '2021-10-06', '2021-10-07', '2021-10-08']

dates2 = ['2021-08-29', '2021-09-05', '2021-09-12', '2021-09-19', '2021-09-26']

np.random.seed(365)
y1 = np.random.randn(len(dates1)).cumsum()
y2 = np.random.randn(len(dates2)).cumsum()

# dataframe with more than a month span
df1 = pd.DataFrame({'date':pd.to_datetime(dates1), 'y1':y1})
df1.set_index('date', inplace=True)

# dataframe with less than a month span
df2 = pd.DataFrame({'date':pd.to_datetime(dates2), 'y2':y2})
df2.set_index('date', inplace=True)

Issue Description

See SO: Plotting two pandas time-series on the same axes with matplotlib - unexpected behavior
Using pandas.DataFrame.plot to plot data with a date range span of more than one month with another data set where the date range span is less than a month, on seconday_y, produces unexpected results in how the API formats and plots the xticks, which results in an incorrect visualization in subplot 0.
In both cases, it is not clear what format the dates have been converted to for plotting.
If dates2 spans at least a month, the issue doesn't occur. (e.g. dates2 = ['2021-08-29', '2021-09-05', '2021-09-12', '2021-09-19', '2021-09-26', '2021-09-29']).

fig, axs = plt.subplots(2, 2, figsize=[12, 12])
axs = axs.flat

print('Note the difference in xticks depending on the date span')
df1.plot(ax=axs[0], title='x-axis is incorrect when the dataframe with\nmore than a month of dates is plotted first')
print(f'axs[0]: {axs[0].get_xticks()}')
df2.plot(ax=axs[0], secondary_y=True)
print(f'axs[0]: {axs[0].get_xticks()}')

df2.plot(ax=axs[1], color='tab:orange', title='x-axis is correct when the dataframe with\nless than a month of dates is plotted first')
print(f'axs[1]: {axs[1].get_xticks()}')
df1.plot(ax=axs[1], color='tab:blue', secondary_y=True)
print(f'axs[1]: {axs[1].get_xticks()}')

df1.y1.plot(ax=axs[2], color='tab:blue', title='More than a month of data')
print(f'axs[2]: {axs[2].get_xticks()}')
df2.y2.plot(ax=axs[3], color='tab:orange', title='Less than a month of data')
print(f'axs[3]: {axs[3].get_xticks()}')

plt.tight_layout()

Printed output

Note the difference in xticks depending on the date span
axs[0]: [18871. 18878. 18885. 18892. 18901. 18908.]
axs[0]: [ 2696  4175  6784  9393 12002 14611 17220 18908]
axs[1]: [2696 2697 2700]
axs[1]: [2696 2697 2701 2702]
axs[2]: [18871. 18878. 18885. 18892. 18901. 18908.]
axs[3]: [2696 2697 2700]

Expected Behavior

Plotting directly with matplotlib.pyplot.plot produces the correct result

fig, axs = plt.subplots(2, 2, figsize=[20, 8], sharey=False, sharex=False)
axs = axs.flatten()

axs[0].plot(df1.index, df1.y1, marker='.', color='tab:blue')
print(f'axs[0]: {axs[0].get_xticks()}')
ax4 = axs[0].twinx()
ax4.plot(df2.index, df2.y2, marker='.', color='tab:orange')
print(f'ax4: {ax4.get_xticks()}')

axs[1].plot(df2.index, df2.y2, marker='.', color='tab:orange')
print(f'axs[1]: {axs[1].get_xticks()}')
ax5 = axs[1].twinx()
ax5.plot(df1.index, df1.y1, marker='.', color='tab:blue')
print(f'ax5: {ax5.get_xticks()}')

axs[2].plot(df1.index, df1.y1, marker='.', color='tab:blue')
print(f'axs[2]: {axs[2].get_xticks()}')
axs[3].plot(df2.index, df2.y2, marker='.', color='tab:orange')
print(f'axs[3]: {axs[3].get_xticks()}')

Print output

axs[0]: [18871. 18878. 18885. 18892. 18901. 18908.]
ax4: [18871. 18878. 18885. 18892. 18901. 18908.]
axs[1]: [18868. 18871. 18875. 18879. 18883. 18887. 18891. 18895.]
ax5: [18871. 18878. 18885. 18892. 18901. 18908.]
axs[2]: [18871. 18878. 18885. 18892. 18901. 18908.]
axs[3]: [18868. 18871. 18875. 18879. 18883. 18887. 18891. 18895.]

Installed Versions

INSTALLED VERSIONS ------------------ commit : 73c68257545b5f8530b7044f56647bd2db92e2ba python : 3.8.11.final.0 python-bits : 64 OS : Windows OS-release : 10 Version : 10.0.19043 machine : AMD64 processor : Intel64 Family 6 Model 60 Stepping 3, GenuineIntel byteorder : little LC_ALL : None LANG : None LOCALE : English_United States.1252 pandas : 1.3.3 numpy : 1.20.3 pytz : 2021.3 dateutil : 2.8.2 pip : 21.0.1 setuptools : 58.0.4 Cython : 0.29.24 pytest : 6.2.4 hypothesis : None sphinx : 4.2.0 blosc : None feather : None xlsxwriter : 3.0.1 lxml.etree : 4.6.3 html5lib : 1.1 pymysql : None psycopg2 : None jinja2 : 2.11.3 IPython : 7.27.0 pandas_datareader: 0.10.0 bs4 : 4.10.0 bottleneck : 1.3.2 fsspec : 2021.08.1 fastparquet : None gcsfs : None matplotlib : 3.4.3 numexpr : 2.7.3 odfpy : None openpyxl : 3.0.9 pandas_gbq : None pyarrow : None pyxlsb : None s3fs : None scipy : 1.7.1 sqlalchemy : 1.4.22 tables : 3.6.1 tabulate : None xarray : None xlrd : 2.0.1 xlwt : 1.3.0 numba : 0.53.1

pandas-dev / pandas