Bitcoin is not safe atm, due to the volatility of the price. But in long term for sure it will be. Laws of the market - demand and supply - always determine. Bitcoin has become increasingly popular, and nothing can stop it now.
Bitcoin will remain volatile for the forseeable future, though. I wouldn't have called it stable (i.e. not volatile) even once during the time it has been bought and sold on exchanges, when you buy into bitcoin you need to accept that it is a volatile asset/currency/commodity and that the price of it will vary wildly.