It is difficult to get straight answers as to why services are cut, or not running to schedule.
I have just been looking at the map and many train lines cross each other, including the services to Victoria from Crystal Palace, and other services that travel through Lewisham to Charing Cross. If this is the reason for the dwindling services, it is not a reason that has been cited before, to me at least. However I am no expert in train lines it has to be said.
In other London boroughs, transport providers are actually challenged and held accountable for delivering scheduled services, which results in better services for residents.
One recent example is below when TFL announced plans to close Balham station. TFL was challenged by the local MP, and this resulted in TFL very quickly proposing another plan. Just shows what can be achieved.