I'm considering buying AE CC, but after evaluating the trial, it seems strange that I can only make 45 seconds long compositions.
Is this a limit in the trial, that will go away if I buy?
You can make much longer comps. Read up on the basics. Composition --> Composition settings.
Definitely no time limit in the trial or paid version of After Effects. As Mylemium points out, adjust the duration of your timeline in Composition Settings.