On the vCenter Server Appliance (vCSA) i have mulitple times seen that the /storage/log runs full, there are multiple reasons that this happens.
But lately the most common reason, is that if you creates support bundles, they are stored in “/storage/log” on the appliance, the problem is that this do not get deleted automatically, this has to done manully.
Even if the Support bundle creation fails, it might still save a partial support bundle on the “/storage/log”.
So my advise is that after you have downloaded the Support bundle, you should delete the file on the appliance.
To delete the support bundles, see this VMwae KB.
NOTE: you don’t have to do the stop/start services if, the vCenter is running perferct, and you delete the bundles proactively.