“Why can’t AI currently experience true feelings? What is holding it back and will it ever be able to?”
To be quite honest, this question is quite complex and quite simple at the same time. Humans, other animals, and even some bacteria, and therefore their consensuses, are very intricate, with that intricacy being one of the main obstacles of the AI field. For example, AI is becoming quite good at recognizing human emotions and can at the same time recreate them. It can recreate the actions, like crying or frowning, but it does not truly feel the emotion. It is faking it. 
But first, before we get too much into this, I must explain what emotion truly is. Emotional reactions are caused by an external stimulus that is captured by our senses, by internal stimulus that could be an alteration in homeostasis (body auto-regulation), or it could be due to our own cognition. Processing the stimulus produces changes at a non-conscious level in the somatic state. If the emotion is sufficiently intense, cognitive, social, contextual and surrounding-related evaluations are carried out, which we refer to as experiencing emotions.  Obviously, that explanation is in laments terms and is quite basic, but it does an alright job of illustrating the complexity of feelings.
But of course, the next step after understanding what emotions are is to incorporate them into AI. To do that, you must create a algorithm that that is capable of copying how human emotions are produced. But still, even with the latest advances in neuro-imaging and neuro-technology, we are still a ways away from making such a complex algorithmic function. The reasons for that are simple and apparent; we face several difficulties. These consist of the problem of reverse inference (there are no specific somatic patterns associated with each emotion), inter-subject variations (no two brains are the same) [2,3], and intra-subject variations (a person’s brain changes and evolves throughout time). The current way of copying how human emotions are produced (Machine Learning) is to use calibration stimuli and then apply automatic learning algorithms. Those algorithms search for the correlations between the emotional responses of the person’s brain in relation to the classification of the picture they are being shown. This algorithm lets the AI learn what emotion the person in question is feeling, lets it replicate how it looks like when someone is feeling that emotion, but is not the human brain, and therefore it can not and is far, far off being able to truly replicate feeling the emotion itself. [2,4]
But all in all, even if we can make an algorithmic function that can replicate the brain’s way of processing emotion, AI will still not be able to truly feel authentic emotions. Human emotions also depend on our perception of the external world and of our inner self. We perceive the exterior world through our senses, while the perception of the interior world depends on homeostasis at a basic level, and, at a more complex level, on our cognition. Not only would AI need to fully understand how to comprehend human emotion, it would have to use the five senses, and it would need to generate all types of emotion that originate from introspection to ultimately feel. Without that, its going to be incredibly difficult for Artificial Intelligence to ever experience the myriad of emotions that human beings feel every day, such as love, happiness and jealousy… But not impossible.
 Minku, L. L. (2019, October 21). Will AI ever understand human emotions? Retrieved from http://theconversation.com/will-ai-ever-understand-human-emotions-70960.
 Will Artificial Intelligence ever have emotions or feelings? (2019, October 7). Retrieved from https://www.bitbrain.com/blog/artificial-intelligence-emotions.
 MRI study: No 2 brains are the same-even among identical twins. (2019, January 23). Retrieved from https://www.healthimaging.com/topics/neuroimaging/no-two-people-have-same-brain-anatomy.
 Regalado, A. (2014, September 19). The Brain Is Not Computable. Retrieved from https://www.technologyreview.com/s/511421/the-brain-is-not-computable/.