Hi,
OK so my question is a customer that is not receiving the emails out of a batch, (the problem you described) do they have that 'Send Method' for Email selected?

When a batch is printed (print/email/fax), only the customers that have the 'Send Method' checked on for that type will be printed. If the customer does not have that type turned on then it will not print.

When you select a single invoice to print, the options for that customer is shown at the top of the dialog. Regardless of the settings on the customer, because you have selected a single invoice you are able to print with any method. This is the reason that you can send a email when it did not work via the batch print method.