Back in the 70s, I knew students who were 'held back' - repeated 4th grade again, etc. I don't think I've heard of that since then. Obviously I'm no longer a 4th grader :) but among people I know with kids, the concept of "held back" never comes up.
Even if you deserve to be 'held back', you get what's called a 'social promotion'.
In 8th grade, there was this big project we (each student) had to do in order to 'pass' 8th grade. The teachers all told us that if we didn't do it, we'd fail 8th grade, but still go on to high school as a 'social promotion'.
I actually had several friends who decided to not do that project, because nothing bad would happen to them if they didn't do it.
In the (public) school my son goes to, people do get held back.
Although it sometimes takes less clear-cut forms than "you fail this course, therefore we make you repeat the entire grade." my mother, for instance, taught at a school (this was ~2000-2006) that kept students perpetually in 8th grade. The school system identified students who were likely to drop out of high school based on grades and behavior and kept them from entering high school to prevent them from depressing high school dropout rates. They would remain in 8th grade until they turned 16 and dropped out.
I was in high school in the 90's, and my classmates frequently failed and had to repeat classes. This usually didn't result in having to repeat an entire grade though, since our schedules were very personalized and classes could be repeated the next year or semester without interfering with the rest of the schedule.
I know that a lot more has to happen in the US in regards to financial reform of public education for kids to be able to repeat grades so liberally, but I think it would do a lot of good.