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](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas.

- [ ] I have confirmed this bug exists on the master branch of pandas.


### Reproducible Example

```python
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](https://stackoverflow.com/q/69516844/7758804)
- 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']`).

```python
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
```python
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]
```
![image](https://user-images.githubusercontent.com/12875240/136818534-607528f7-0d35-44b6-90db-71b4b64502be.png)


### Expected Behavior

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

```python
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
```python
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.]
```
![image](https://user-images.githubusercontent.com/12875240/136818841-eb834721-9e54-48a6-9e5b-539291848c37.png)


### Installed Versions

<details>

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

</details>
