BUG: Freq argument lost using `pd.infer_freq`
- [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.

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

---

#### Code Sample, a copy-pastable example

```python
import pandas as pd

# reference, works: 2 normal days.
i0 = pd.date_range('2020-09-24', '2020-09-26', freq='H', closed='left', tz='Europe/Berlin')
pd.infer_freq(i0)  # 'H'   (i0.freq == '<Hour>')

# problem, does not work: summertime to wintertime changeover.
i1 = pd.date_range('2020-10-24', '2020-10-26', freq='H', closed='left', tz='Europe/Berlin')
pd.infer_freq(i1)  # '' <-- !!!!!    (even though i1.freq == '<Hour>')

# for completeness, works: wintertime to summertime changeover
i2 = pd.date_range('2020-03-28', '2020-03-30', freq='H', closed='left', tz='Europe/Berlin')
pd.infer_freq(i2)  # 'H'     (i2.freq == '<Hour>')
```

#### Problem description

Even though `i1` has the frequency attribute correctly set, `pd.infer_freq(i1)` returns an empty string.

#### Expected Output

`'H'`, just like when using `i0` or `i2`.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : db08276bc116c438d3fdee492026f8223584c477
python           : 3.8.5.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.18362
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en
LOCALE           : de_DE.cp1252

pandas           : 1.1.3
numpy            : 1.19.2
pytz             : 2020.4
dateutil         : 2.8.1
pip              : 20.3
setuptools       : 50.3.2.post20201202
Cython           : None
pytest           : 6.1.2
hypothesis       : None
sphinx           : 3.2.1
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : 1.0.1
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.19.0
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.2
numexpr          : None
odfpy            : None
openpyxl         : 3.0.5
pandas_gbq       : None
pyarrow          : None
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.2
sqlalchemy       : 1.3.20
tables           : None
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : None
numba            : None

</details>
