2CNF with 3 variable occurences
The following is unsatisfiable:
$$
(x \lor y) \land (x \lor \lnot y) \land (\lnot x \lor z) \land (\lnot z \lor w) \land (\lnot z \lor \lnot w) \land (y \lor w).
$$
This contains every variable exactly three times, not all of them of the same polarity. If you allow variables to appear less than three times, you can drop the last clause $y \lor w$.