If you look at the definition of StringPartition, you'll see that it is just a stub loading a package, not a real function (in a fresh kernel, of course):

ClearAttributes[StringPartition, {Protected, ReadProtected}]
Definition@StringPartition

StringPartition := System`Dump`AutoLoad[Hold[StringPartition], 
                                 Hold[StringPart, StringPartition], "StringUtilities`"] /; System`Dump`TestLoad

The package redefines StringPartition and protects it again:

StringPartition;
ClearAttributes[StringPartition, {Protected, ReadProtected}]
Definition@StringPartition    

StringPartition[StringUtilitiesDump`args___]:=With[{StringUtilitiesDump`res=StringUtilitiesDump`oStringPartition[StringUtilitiesDump`args]},StringUtilitiesDump`res/;StringUtilitiesDump`res=!=$Failed]

This explains the behavior you observe. The workaround is to preload the package before making any new definitions as I made above. But remember that modifying built-in functions is dangerous and isn't recommened until you know exactly what you do...

I have a quite interesting observation of this function as well:

In[1]:= Attributes[StringPartition]
Out[1]= {Protected, ReadProtected}

In[2]:= Unprotect@StringPartition
Out[2]= {StringPartition}

In[3]:= Attributes[StringPartition]
Out[3]= {ReadProtected}

In[4]:= StringPartition[n_Integer,d_Integer]:=Function[str,StringPartition[str,n,d]]
During evaluation of In[4]:= SetDelayed::write: Tag StringPartition in StringPartition[n_Integer,d_Integer] is Protected.
Out[4]= $Failed

In[5]:= Attributes[StringPartition]
Out[5]= {Protected,ReadProtected}

Somehow the function is automatically protected again. It does not happen for Log in this online doc