id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1006413760,I_kwDOAMm_X847_KfA,5815,Inconsistent dropping of `DatetimeIndex.freq` attribute from `DataArray`s index.,4806678,closed,0,,,7,2021-09-24T12:28:27Z,2023-08-23T13:41:17Z,2023-08-23T13:41:17Z,CONTRIBUTOR,,,,"<!-- Please include a self-contained copy-pastable example that generates the issue if possible.

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**What happened**:

Indexing on `DataArray`s sometimes produce inconsistent behaviors on `DataArray`s indexed with a `DatetimeIndex`.
There are cases (see code below) where copied versions of the array obtained with `DataArray.copy()` loose the index's `freq` attribute when calling `isel()`, whereas copied versions obtained using `DataArray.sortby()` do not.

**What you expected to happen**:

I would expect the `freq` not to be dropped from the axis when indexing the `DataArray`. Or at least, if it is dropped, it should _always_ be dropped, and not depend on how the `DataArray` has been obtained (i.e., it should not depend on whether it's a `copy()` of another array).

**Minimal Complete Verifiable Example**:

```python
import xarray as xr
import pandas as pd
import numpy as np
from pandas.tseries.frequencies import to_offset

freq = to_offset('MS')
time_index = pd.DatetimeIndex([pd.Timestamp('20130101') + i * freq for i in range(10)])

xa_orig = xr.DataArray(np.random.randn(10), 
                       dims=('time'), 
                       coords={'time': time_index})

xa_copy = xa_orig.copy()

xa_sorted = xa_orig.sortby('time')

# Set freq on all DataArrays:
xa_orig.get_index('time').freq = freq
xa_copy.get_index('time').freq = freq
xa_sorted.get_index('time').freq = freq

# Print to confirm the freq is set correctly:
print(xa_orig.get_index('time').freq)
print(xa_copy.get_index('time').freq)
print(xa_sorted.get_index('time').freq)
```

Output (OK - as expected)
```
> <MonthBegin>
> <MonthBegin>
> <MonthBegin>
```

Now, try some indexing using `isel()` on slices:
```python
print(xa_orig.isel({'time': slice(0, 5, None)}).get_index('time').freq)
print(xa_copy.isel({'time': slice(0, 5, None)}).get_index('time').freq)  # freq is dropped!
print(xa_sorted.isel({'time': slice(0, 5, None)}).get_index('time').freq)
```

Output (Not as expected: `freq` is dropped inconsistently, only on the _copied_ DataArray)
```
> <MonthBegin>
> None
> <MonthBegin>
```

Now, try the same using `isel()` on lists:
```python
print(xa_orig.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
print(xa_copy.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
print(xa_sorted.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
```

Output (Not as expected: `freq` always dropped)
```
> None
> None
> None
```

**Anything else we need to know?**:

**Environment**:

<details><summary>Output of <tt>xr.show_versions()</tt></summary>

INSTALLED VERSIONS
------------------
commit: None
python: 3.8.5 (default, Sep  4 2020, 02:22:02) 
[Clang 10.0.0 ]
python-bits: 64
OS: Darwin
OS-release: 20.5.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: None
LOCALE: (None, 'UTF-8')
libhdf5: None
libnetcdf: None

xarray: 0.19.0
pandas: 1.2.3
numpy: 1.19.5
scipy: 1.6.2
netCDF4: None
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: None
distributed: None
matplotlib: 3.4.1
cartopy: None
seaborn: None
numbagg: None
pint: None
setuptools: 49.6.0.post20200814
pip: 21.1.3
conda: None
pytest: None
IPython: 7.22.0
sphinx: 3.2.1


</details>
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