Hi Kostya,
... what an idiot am I! :p ... during one of the updates (yes, Cyanogenmod - sorry for using an acronym), "sync" got disabled. *sigh*. Sorry to waste your time.
To help other people from my mistake, here's how I found the problem ...
First I looked through the `log-AquaMail.txt' file. What I did was enabled debug and ensured the debug file was created. Next, I disabled debug and emailed myself the log file.
I grok'd through the file and found `Prefs AutoSync setting is OFF, no sync' Oops!
Next, I went back to AquaMail, `Mail, receiving > System settings' and switched it from `Observe all' to `Sync even when "Auto-Sync" is off"' And voila! I could see the AquaMail icon in my `Notification' tray.
To enable `sync' in CM I take the easy way out. I added a `Tile' under the `Quick Settings panel' To do this, do the following: Settings > Interface > Quick Settings panel > Tiles and layout. Click on the `+' and add the `Sync' tile.
For the truly uninitiated (hey, we all have to start at the beginning), to get to the `Quick Settings panel', pull down on your `Notification' tray and if you don't see it, switch by dragging your finger either at the bottom grey (CM 11) bar or at the upper right icon (looks like a little person).
After I enabled sync, I went back to AquaMail and reset `Mail, receiving > System settings' back to `Observe all' And all is well.
Cheers,
-pablo