A ZAB Center Controller reported ATC lost communications with an aircraft that subsequently flew below the Minimum Vectoring Altitude.

Narrative

Aircraft X was on an IFR flight plan traveling west bound at 100; nothing wrong; just flying along. I had split the sector 21 to sector 23 and informed the controller that he was on the CVS altimeter; at that time he was out of my airspace with roughly another 15-20 minutes to fly west bound. No conflicts; but I guess the aircraft went NORDO; because of poor coverage in the area and went through a 108 block. I was made aware of this an hour or so after I had gotten off sector. At the time I left communication with aircraft was fine as the aircraft wasn't too far away from the border with CVS approach; but in that corner near CNX it's been a well known radio coverage issue for 15-30 years and hasn't been fixed and I didn't have the sector anymore to fix the issue of not going over CNX.The frequency in question; 126.85 has been the subject of numerous; to the point of hundreds if not thousands; yes thousands; of reports to supervisors and tech ops personal about the lack of coverage in that particular area. Maybe fix the radios so that we can communicate with the aircraft when we need and give clearances that might save someone's life.