For a bank to create a long-term relationship with a customer that is based on mutual long-term value creation. what is this fundamental driver?

Agree with both answers. However intimacy by itself and good service alone may not actually provide satisfaction  and hence loyalty. By being intimate you will probably realise that quite often clients shop around and look for price leadership for deposits and the lowest rate for advances with the risk and threat of a  'bye bye charlie' if you do not provide satisfaction.  On overall basis I believe in a periodic delight in service so as to ensure long term loyalty.

The fundamental for a any kind of long term relationship is Trust. Trust building is a process by giving committed and timely hassle free services. But the worst and the bitter truth is that many times customers are more demanding so in that case be transparent and truthful without any communication gap. 

I will sum it up in5 key areas;1) Start with a differentiated Memorable World-Class Customer Service Experience and introduce the customer to your team members.2) Show the customer the Benefits and Value of doing business with you personally and the bank to gain customer's trust.3) Regularly connect and follow up with your customers to strengthen the relationship, uncover new mutual opportunities and quickly resolve any dissatisfactions by offering solutions.4) Be aware of market competition and what set your bank apart from the rest.5) Train and prepare to overcome objections which will lead to more cross-sell, growth in the relationship and retain and satisfy your customers.

Keeping service promise and Providing good service will go a long way in retaining a customer

yes , we call it customer intimacy .

Good Service is the best tool to create a long-term relationship with a customer that is based on mutual long-term value creation