Why doesn't Kelly Chambers send me a message after the suicide mission?

Solution 1:

There's a possibility it may not be available based on one of your dialogue choices during the suicide mission. From the talk page on the Mass Effect Wiki:

I think I figured out why it wasn't working in my case -- I replayed the suicide mission and the only thing that I know I changed was when you rescue the crew you get the choice to say "I wouldn't leave you behind" or "I didn't come for you", The first playthrough I chose the 2nd option and I think that pissed her off (was an accident, damn spacebar). After replaying and choosing the first option I got the email. --74.248.177.233 01:36, June 21, 2011 (UTC)

Had the same problem after my first run. What worked for me: After returning from the suicide mission (a second time), I first checked the private terminal in my cabin, so all old messages were marked as read. I then spoke to her first, comforting her. After that I made the tour around the CIC, spoke to Joker, Mordin, Jacob, returned to my terminal, she informed me about the message again - and there it was. --46.223.161.247 16:57, July 17, 2014 (UTC)

There are other possible fixes/issues discussed on the page, most notably under the heading of "Frustrating".

Hopefully one of the solutions here can work for you.