Asking anyone to outright state the future of technology is simply bad faith business - especially as we have no idea exactly what your project entails.
The product is supported until next year, after which you're on your own. If your project is a simple 2D app that has minimal dependencies, it's probably going to be okay, barring some fundamental web architecture changing, which is often highlighted well in advance.
Having used C2/3 for almost a (oh God) decade, the engine very rarely actually breaks - it's often specific feature on a specific platform - depending on what this is, you could refactor your project to work around it.
I would say your best bet would be to port your project to C3 - there's a whole community of us that would be happy to help, and you've got roughly a year in which to do it.
More information could help here - if it's a kiosk style bit of software, you could fairly easily simply lock the hardware to a specific browser and never update it - plenty of museums have done this with Flash based projects, and Director before that.
Thanks for the input...
We were developing it to be a SAAS for language schools, and heavily using it in our own school.
I wasn't asking to predict the future. I asked "Do many compatibility issues come up?" He vaguely answered my question. It seems we have to make a very big decision now.
My team and I all purchased c2. We came over from unity two years ago. Turns out it was my error for misunderstanding the meaning of "updates for life". Silly me. How could I have missed that! Haha. Of course that means "Two more years, then you're on your own."
Ah well. This is business as usual I suppose.