In Shmuel 2 Chapter 15 Paragraph 20 Kind David singles out Itai and tells him to either go back or to leave him.. Was he scared that Itai would betray him? or did he fear for his and his brothers safety?
Judaica Press summarizes Rash, Radak, Abarbanel, and Metzudas David to say that Dovid Hamelech was telling him that if he stayed behind or traveled on his own, Avshalom would leave him alone and he would be safe. On the other hand, if he insisted on staying with Dovid Hamelech, he would not only be in danger, but he would be unable to find a safe house among the residents of the kingdom. Since Dovid Hamelech did not have adequate supplies, he would be unable to help Itai. Thus, he should go on his own path and if Dovid Hamelech succeeded in defeating Avshalom, he would remember what Itai had attempted to do.
Note verse 21 says that Itai refused, so DovidHamelech had him go with the group that contained the children and the vulnerable people so that Avshalom (concentrating on Dovid Hamelech) would not chase them.
Professor Wright argues that Ittai was a soldier of fortune so to speak and thus his loyalties, and perhaps the loyalties of the men from Gath whom he represented were in question.
As a side note, Professor Wright points to commentary of Tama Cohn Eskenazi who notes the similarity in language between David's exchange with Ittai and Naomi's attempt to dissuade Ruth from joining her. It appears that in the later story there are also elements of probing the sincerity of the follower which come in to play.