Is Theatre A Dying Art Form?

Yes, but it has been dying and reviving since the advent of the film and the television, but somehow people still enjoy acting on stage, and people still enjoy going to the theatre, they see some value in communing with others in a shared environment, taking part in a shared experience.

Theatre was essentially a way of expressing things, through movement, then through movement and sound, and finally an actor appeared, then a group of actors. Theatre has been banned during the Puritan rule of England. It's not surprising, the theatre can be challenging and has an amazing way to communicate to people and therefore people think its dangerous. During the Eighties and the early Nineties, the Sun newspaper and the Conservative government tried to kill the theatre in Britain, they did this by portraying the theatre and its folk as money-grabbing 'luvvies', who were over and above necessity. It didn't work because it isn't true and despite repeated attempts to kill it through a lack of funding, it is still alive, the heart is still beating.

In general, yes.  The increased availability of entertainment options makes it harder and harder for theater to compete.  Movies started the trend away from stage.  Broadcast television amplified it.  Then cable and satellite took it further still.  Now high speed networking and the multiplicity of media options made available by networking and computing technologies are making cable look trite.  When people can sit at home and watch exactly what they want to watch and/or listen to whatever music they like online, there is dwindling incentive for them to take part in a live theater (or live music, for that matter) setting,

Theater audiences have become narrower and narrower in terms of demographics.  It won't take much of a shift in economic or social conditions for theater to take it on the chin.  In fact, living in Chicago, it's obvious that in large part, theater is supported by people who harbor dreams of acting, directing, writing, and/or doing technical work for the stage themselves.

I personally enjoy stage theater, but even I can see the shrinking of audiences.  Understand that it is probably easier to make a living working in internet media (say, doing 5-15 minute webcast series) than in live theater.