How do you stop Pandas DataFrame.groupby() changing dtype from object to float when group column only contains nan values?

When I run the following code:

import numpy as np
import pandas as pd

df = pd.DataFrame({"S": ["xx", np.nan, np.nan], "V": [1.1,2.1,3.1]})
a = df.groupby(["S"], as_index=False, dropna=False).sum()
print(a.dtypes)

I get the following result, as expected:

S     object
V    float64

However, if I select a subset of rows that happen only to contain nan values:

df2 = df.iloc[1:,:]
a2 = df2.groupby(["S"], as_index=False, dropna=False).sum()
print(a2.dtypes)

the S column in the resulting DataFrame is converted to a float which breaks subsequent code.

S    float64
V    float64
dtype: object

Is there any way of preventing this inferring of types and always keep the original type of S?