Intermittent error fetching value from multi-indexed dataframe
- [x] I have searched the [[pandas] tag](https://stackoverflow.com/questions/tagged/pandas) on StackOverflow for similar questions.

- [x] I have asked my usage related question on [StackOverflow](https://stackoverflow.com).

- See [this question](https://stackoverflow.com/questions/65927344/accessing-dataframe-with-multiindex-with-date-intermittently-failing) and [this question](https://stackoverflow.com/questions/65937092/read-pickle-failing-stochastically).

#### Question about pandas

I have a dataframe with a multiindex from which I am attempting access a row from. However, it is seemingly failing stochastically on around 1/10th of runs. I see this behaviour both locally and on prod. The dataframe can be recreated with the following:

```python
from datetime import timedelta, date
import pandas as pd
import pytz
from pandas import Timestamp

utc = pytz.UTC

data = {
    "date": [
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).replace(minute=59, second=59, microsecond=999999),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date(),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date(),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date() + timedelta(days=1),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date() + timedelta(days=1),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date() + timedelta(days=2),
        Timestamp("2020-06-03 15:00:00").replace(tzinfo=utc).date() + timedelta(days=2),
    ],
    "a": ["alpha", "alpha", "beta", "alpha", "beta", "alpha", "beta"],
    "b": [100, 100, 100, 100, 100, 100, 100],
    "c": [100, 100, 100, 100, 100, 100, 100],
    "d": [0, 0, 0, 0, 0, 0, 0],
    "e": [100, 100, 100, 100, 100, 100, 100],
    "f": [0, 0, 0, 0, 0, 0, 0],
    "g": [0, 0, 0, 0, 0, 0, 0],
    "h": ["A", "B", "C", "D", "E", "F", "G"],
}
df = pd.DataFrame(data)

breakdown = df.groupby(["date", "a"]).sum()
done = breakdown.loc[date(2020, 6, 3), "beta"]
```

I do not know if it is my incorrect usage that is causing this behaviour or a bug.

I originally encountered the issue on `pandas` `1.1.4`(*) with the error:

```
TypeError: '<' not supported between instances of 'int' and 'slice'
```

and on `1.2.1`(**) I see the same intermitent errors but with the error message:

```
KeyError: 'beta'
```

#### Version info

(*)

```
INSTALLED VERSIONS
------------------
commit           : 9d598a5e1eee26df95b3910e3f2934890d062caa
python           : 3.9.0.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Mon Aug 31 22:12:52 PDT 2020; root:xnu-6153.141.2~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.UTF-8

pandas           : 1.2.1
numpy            : 1.19.5
pytz             : 2020.5
dateutil         : 2.8.1
pip              : 21.0
setuptools       : 49.6.0.post20210108
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None
```
(**)

```
INSTALLED VERSIONS
------------------
commit           : 67a3d4241ab84419856b84fc3ebc9abcbe66c6b3
python           : 3.9.0.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Mon Aug 31 22:12:52 PDT 2020; root:xnu-6153.141.2~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : None.UTF-8

pandas           : 1.1.4
numpy            : 1.20.0
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 20.3.1
setuptools       : 49.6.0.post20201009
Cython           : None
pytest           : 6.2.1
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : 1.1
pymysql          : None
psycopg2         : 2.8.6 (dt dec pq3 ext lo64)
jinja2           : 2.11.3
IPython          : 7.20.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.4
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.6.0
sqlalchemy       : 1.3.17
tables           : None
tabulate         : 0.8.7
xarray           : None
xlrd             : None
xlwt             : None
numba            : None
```
