What's happening to carbon electrodes?
Pencil leads aren't pure graphite, they're generally graphite powder with various polymers to hold them together and make sure they have the correct hardness (after all, you wouldn't be able to use them to write if they didn't leave graphite on the paper or if they crumbled under slight pressure. This is why the much more rigid glassy carbon is a popular material for carbon electrodes. My guess is that there's no reaction with the electrode happening but gas being produced is causing mechanical damage to the electrode. If you work at less extreme potentials, you might be able to reduce this effect. Otherwise, pure graphite rods should be more durable. Of course, if you're using pencil leads, they're obviously cheap to replace so it might be easier to just use them until they fall apart, then switch to a new one.