I have only apologized once through email and she did respond that an apology is not necessary. HOWEVER there have been quite a few times where I have written an email that I she didn't respond to and upset I didn't. Eventually she did email me back but it may be days later. With an apology and an explanation (she was sick, had computer issues, was busy and just didn't have time to read her email etc).

I would be upset if she didn't respond at all because she wanted to discuss the issue at the next session. It has happened a couple of times where T wanted to discuss the issue in session but she will respond that it is a difficult discussion so we will discuss it at my next appointment.