The dialog informing you that the application has “unexpectedly quit” is generated by OSX to inform you that the application (in this case, Cubase) has suffered a fatal crash.
This can have many causes. Often it is simply caused by some program glitch. These are very hard to track down because they are generally not repeatable. With software that use plug-ins, these are more than often the cause of the problems. For example Cubase (v7.5 in particular) has a nasty habit of “unexpectedly quitting” when plug-in are removed in the MixConsole. Here is a discussion about this subject:
Although there are reports of people experiencing this problem with VST3 plug-ins, my impression is that it only happens with VST 2.x plug-ins. Since you say that your problem started when you began a new project, ask yourself if you are using any new plug-in(s) [VST or VSTi] with this project. If you are, try not working with these for a while and see if the problem goes away. If it does, see if there is a newer update available. Otherwise, report the problem to the plug-ins manufacturer.
Also, if there is a choice between a VST 2.x and a VST3 version of a plug-in, I always install the VST3 version. And I never install both.
There will never be a 100% crash-proof piece of software. The closest thing, I believe, Steinberg has come was Cubase v1.0 on the Atari (about 20 years ago). That one was just about impossible to crash. However there are two important steps you can take to minimize the risk of loosing work from a crash.
Make sure that you have Auto Save activated in Preferences/General and set a relatively short “Auto Save Interval” (I have mine set to 10 minutes). This feature will not interfere with you working as a) it all happen in the background, and b) the auto-saving is suspended while recording takes place.
Always hit Save when you have done something, such as record a take or made a major edit. Just to be in the safe side.
Hope this will assist you in sorting out you problem.