A lot of times when I singer misses a lot of concerts, the fan are disappointed, but very few would be so enraged as to completely disown the singer. The fans are fans because they like music. Not because they like the singer and his style, and the music will still be good. They may be dispointed, but that would be short lived.
Robin Rhicke wil still have many fans even though he is missing some scheduled concert dates because of his separation from his wife Paula. He has made big headlines this past year and is very popular right now with the younger crowd. They like his music and wan to see him in concert.
Every musician of any renown will have two sets of fans. The marginal fans may fall away because of missed concerts, feeling that Robin Thicke does not appreciate them as an audience. However, his hardcore fans will stick with him regardless of his antics. Anyone who doubts this needs only to see the videos of adoring fans cheering for Michael Jackson as he was being tried for child molestation.
Yes, fans will still support Robin Thicke in spite of his missed concerts, because people understand that sometimes musicians and entertainers have life happen and sometimes they have to miss concerts. When they make concert dates, they understand that sometimes extenuating circumstances will prevent you from making it to the concert. Robin Thicke had some circumstances happen.
I definitely think that while fans will be upset that he missed some of his concerts, I think they also know that he canceled them for personal reasons instead of it being due to irresponsibility. I think his fans will still be willing to support him despite the recent issues.