Not sure of the reason it is not feasible through the SSMS GUI for the error log but as some posted before me it is also possible to modify the error log location.
--stop the service
in sql server configuration manager:
right click on the servic of the sql server you want to modify. Select “properties”
In the properties screen, select the “advanced” tab
--modify the log position
Modify the line contained at “startup parameters”.
The part of the line to modify is the value after the –e.
--restart the service
Once this is done, restart the sql server service.
If you enter erroneous location in the startup parameters, your service will fail to restart so make sure you keep a copy of your original string in case.