The major difference between ESB and EAI is not Single-Point-Of-Failure.
Having said that, if the ESB Bus fails then, yes, it is a point of failure. Ultimately these are just applications in your infrastructure and whether they are a single point of failure or not is dependent on their deployment (eg. clustering) and not on the underlying conceptual integration pattern.
Personally I would classify ESB (Enterprise Service Bus) as a type of EAI (Enterprise Application Integration). Many companies trying to sell you a product instead of a concept would argue differently.
ESB is just the new pattern for EAI instead of Hub-Spoke. I wouldn't get too caught up in the differences. When you dig into it they are few and far between.