The challenge for twitter is that they were always compared to Facebook and the two, while competing for the same marketing dollars, are delivering different products for different use cases which ultimately means different levels of user numbers and engagement.
Stock markets are speculative, so investors trade on the story and the fundamentals on a sliding scale, in the case of twitter it's fundamentals aren't strong without a road to profit, one that they are also quite far away from, and in terms of story being compared to FB which now has 4x more users and continues to grow doesn't allow it to create a story that investors can rally behind or support it.
Ultimately the main issue with Twitter was lack of leadership and decision making and the failure to acquire Instagram.
If Instagram was a part of Twitter then they would have a secondary social network, that today (although with FB integration) has already outpaced them in terms of user numbers and continues to grow.
That failure is why they are where they are currently. They haven't been able to do a large strategic acquisition that really pushed their company forward and the ones that they have done were mainly add-ons and smaller in comparison that were never able to stand on their own.
Kudos to Mark and Facebook for being decisive and pulling Instagram from out under Twitter, but if Twitter want to get the deal done they should have led with a Billion not $500MM and the deal would have been theirs.