See - How to set the home page

Set a webpage that requires a login, thus bringing up the Master Password dialog window, as one of your homepages so that every time you open Firefox the Master Password window appears. One you enter the Master Password you won;t be asked for it again during that session.

Or look for an add-on that modifies how the Master Password works in Firefox. AMO search for "Master Password"

When you start Firefox, if you use Sync, you will within about a minute get prompted for your master password. Otherwise, I wouldn't expect it to pop up when you weren't going to a login page.

If you are in the habit of closing Firefox frequently so that you experience startup multiple times a day, consider keeping a Firefox window open longer so the prompts are less frequent.

thank you, but the problem is that prompt appears randomly. Maybe after 10 secs after start or maybe after 2 hours. I think sync function chooses this moment. As a workaround I install StartupMaster add-on. Prompt appears immediately after start now.