One problem related to engine burning oil has been reported for the 2012 Honda CR-V. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2012 Honda CR-V based on all problems reported for the 2012 CR-V.
Vtc actuator grinding on cold start. Reported to Honda. Paid to have it replaced out of pocket at a cost of $1443. 83 on 9/24/18 at 111,863 miles. At 122,000 miles started having high oil consumption. After several misdiagnosis by hare Honda, determined same issue as 2011 TSB a12-089 problem with sticking piston rings. Requires full engine rebuild quoted at $2000. If not fixed can cause engine failure.