Limits are not the problem
In ten years of teaching this I have had two students who could not understand what a limit is. I have had dozens who could not simplify the expression inside one.
The three that come back
Trig identities, log rules, and factoring by grouping. Every one of them was taught a year or two earlier and passed with a C, which is exactly the grade that lets a gap through without anybody noticing.
Diagnose backwards
When a student misses a derivative question, read the last line of their work before the first. The calculus is usually right the whole way down to a piece of algebra from three courses ago. Marking the question wrong teaches nothing; marking the line does.
Going back is cheaper than a retake
Six weeks of pre-calculus alongside the course, not instead of it. Retaking calculus costs a semester and most transcripts keep both grades.