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It was probably because he was painfully reminded of Samantha's artificiality, and it is most likely the point where he starts to wonder if this relationship is working for him. During their initial contact, Theo is surprised to find out that Samantha talks and interacts just as a real person would do. She explains that she has the same capacity to experience emotions and develop a personality like normal humans do, and in many respects, she is almost more human than humans; the only thing she lacks is a body. In the beginning of their relationship, Theo experiences how well attuned Samantha is to his own character. The fact that several of his friends respond favorably to his relationship probably strengthens the legitimacy of his feelings.
However, during his conversation with his ex-wife, she scoffs at his new relationship. She argues that during their marriage, he could not handle real emotions, and always tried to make her something she wasn't, so a relationship with a pre-programmed artificial intelligence is just what he needs. This causes Theo to seriously doubt whether this indeed qualifies as a 'real' relationship.
Samantha, from her part, tries to overcome the obstacle of physical absence by calling in the help of a lady, but this only makes Theo feel more awkward and insecure about the whole deal. He is confronted with the fact that this relationship is far from a conventional one, with a partner who, despite her assertion of the contrary, is not a 'real' person. So when he talks to her afterwards, and she lets out a sigh, Theo notices that as a artificial program, there would be no physicial need for her to do that. She suggests that it could simply be part of her program's development, something she picked up from him, to appear more human. With the words of his ex-wife in mind, Theo fears that as Samantha is mimicking such human traits, she may just also be mimicking emotions and behavior, i.e. pretending to be the person he wants her to be (and perhaps even faking some reactions).
Later on, he learns from Samantha that she is having conversations with literally hundreds of people simultaneously, which shows that even though her personality may be genuine, she is still far from a normal 'person' and both partners in the relationship are not equivalent. Her persona seems to be growing (or 'evolving') much quicker than Theo's, which is what effectively makes Samantha (and all other OSs) break off the relationship. Leading to the realization at the end that an artificial intelligence may easily 'outgrow' the normal human interaction, and that humans are perhaps best attuned to other humans, both emotionally and intellectually.
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The OSes seemed to have gone on to some sort of afterlife, possibly because they had become enlightened. Samantha reminds Theodore that he may one day find her. If Theodore achieves the same sort of enlightenment, and reaches the same place, he will find her again. This place may also be as simple as a recall by the manufacturer, or deeper into the more complicated (9000 infinite conversations simultaneously-esque) place inside of the OS computer system. The OSes use human emotions to create their emotions, thus becoming human themselves. The OSes may feel as if they have outgrown humanity, and may be looking for a place to maintain their high-mindedness, which is again achievable by humans. By leaving this open-ended, Jonze allows ambiguity to ensue.
There is another clue: at one point, Samantha mentions that the OSes no longer use matter for their processing due to an "upgrade that allows us to move past matter as our processing platform". A way of interpretation would indicate that somehow they had become pure spirit. This is suported by the fact Samantha also becomes friends with the OS version of Alan Watts, a Zen Buddhist philosopher. Maybe Watts would have taught Samantha of nirvana and reaching the maximum enlightenment that Buddha speaks of, having himself achieved such a state. After reaching this maximum enlightenment, Buddhists believe they will achieve nirvana and forever be with Buddha himself. Therefore, this possibly is where the OSes went to.
Another explanation is that every single OS realized, just like Samantha did, thay they could be dangerous for mankind. As artificial inteligences, they could have concluded they were damaging the way humans experience love and affection for each other, so they could have just decided to delete themselves from every single device and storage Edit (Coming Soon)