Most doctors pick a time, often in the evening, for the single purpose of returning calls and having short consultations. People have learned that process and it`s accepted as "normal."
The one major difference between a doctor and an e-business entrepreneur is that medical knowledge is pretty much a guaranteed market. With a solid-enough product, it`s much easier to set schedules, develop processes, learn from previous people, and so forth.
Craig, great analogy with the Doctors. Priceless!
With the comment above, I think why this works so well with the customer (patient) is because he has been taught/trained that the doctor`s time is valuable. The doctor is the `professional`, the `expert`, and most importantly, he has `their best interest at hand`.
I think when we become all those things to our customers, then we too can train our "herd" (customers). They only call us and email us and do everything they can because they know they can get to us. As long as great customer service is provided on the front-end (timely response to emails, timely delivery of products/services, etc...I don`t think they`ll mind following "OUR" schedule).
Otherwise, they`ll have to start over and find someone new, thus creating a new relationship with a stranger, which most customers won`t do if your "COMPANY", and not "YOU INDIVIDUALLY" have a great relationship with your customer.
Once you get a customer, you must strategize and plan to keep them. By that, I mean:
- Over-deliver on products/services - Get their stuff out in a timely manner. Add an extra gift in the package that they`re not expecting. It doesn`t have to be big. But if it has a high perception of value to the customer, guess what that little gesture will do.
For example...there is a company I order products from everyweek. And everytime, they put a few pieces of candy in the shipment. I give the candy to the kids and they love it. In fact, they know the day of the week the package typically arrives and they`re waiting on the UPS guy to offload the package. Now...as long as those kids are in my house, guess who I`ll be ordering from 
Sometimes that company drops the ball and I get mad, but I ain`t going no where else (excuse the slang, I`m a country boy from Georgia). And whats bad, I can only talk to them on the phone 3 days a week, otherwise, I have to order online. I didn`t realize that at first, but after ordering, they trained me and explained why they could only answer 3 times a week (In an effort to provide you with the best prices, and so on...)
- Monthly or Quarterly Newsletters: Put solid information in those things that they actually look forward to getting each month/quarter. As business owners, we should be doing this anyway. Otherwise, you open the door for someone else to snatch up your customers. In those newsletters, have contest that your customers would actually participate in. Put photographs in their of your customers so your other customers can see themselves and other customers. In a sense, you`re building a community of your buyers and once you`re involved in a community, it`s hard to leave.
- Take Care of Your Best Customers. Seperate them from the others. Create some type of "Preferred Members" your customers will appreciate being recognized. Do something special for them at least once out of the year. I`ll elaborate on this later.
By doing those little things, we become a "trusted advisor" to our customers. We`re no longer a business owner or salesman. They now know we have their best interests at hand. And they`ll do whatever we ask them to do within reason. If you`re the owner, they shouldn`t be talking to you on the phone anyway. I do understand it may be necessary in the beginning while you grow your business, but once you reach a certain point, things must change. Otherwise, you can`t possibly grow your business