Twitter can be profitable, how much profit is a harder question. Already they have the market entirely in their ecosystem, just watch any mainstream TV show or news report to see 'hashtag' has entered common language. Trying to see Twitter as some multibillion dollar company comparable to Google or Amazon seems a lot less likely.
Twitter does have a chance at being profitable for the long term. Personally, being a college student and not having cable television, Twitter is an instant source of news for me. Following local news stations is crucial during times is so important especially during weather situations. It can provide updates to the minute as to what's going on without any interruptions. I can also know if something is going on in my community, or University that is potentially dangerous that would get to me faster than if it would on the news stations. Twitter is not going anywhere.
No, Twitter has no long term prospect of being profitable. The valuation for Twitter has become frothy and excessive since its IPO. They cannot reasonably be expected to achieve profitability given their existing financial metrics. At best, they may add value to another firm via an acquisition that will break apart the company and leverage only the value addition of the social messaging service.
No, Twitter does not have a chance at being profitable for the long term. As long as people are using it to spam the world, the chance for success is small. Twitter needs to do a better job of blocking spam out, and they will get a chance to fix the damage that has been done.