ZLC Controller reported having communication problems with an aircraft and later learned that this is a known issue with the radio.

Narrative

Radio issues continue to affect Sector 41. I took radar on Aircraft X from ZSE and I believe I heard the standard 2" callout from the wingman as they change frequencies but never heard Lead's check-on. A frequency was remote muted due to some issues; so I turned it back on and tried Aircraft X again with no response. Called ZSE and they tried Aircraft X with no response. I then broadcasted on VHF Guard for Aircraft X and Aircraft Y in the area at 360 keyed up to say that Aircraft X was on frequency. I change radio configurations to every combo (primary/secondary) I could think of over a few minutes and never heard them. Aircraft X travelled about 75 miles in my airspace before I finally received a radio check transmission from them. When I answered; they said they heard me loud and clear and requested a descent. I coordinated their descent with the low controller and when I issued it I did not get a readback. I issued it several times on different transmitters; never receiving a readback; when I went to ask for an aircraft to relay I observed the flight descending. I then shipped them to the low sector; again not receiving a readback.Around the same time I worked Aircraft Y across the northeast corner of my airspace. When they checked on they were weak but said they had me loud and clear. When it came time to ship them I could not reach them. Had to try multiple transmitters before Backup Emergency Communications (BUEC) finally reached them; which is unusual.I reported Aircraft X as being half NORDO to the Supervisor and he went and reported it to Operations. When he came back he said they advised it was "a known problem."I'm not sure how I'm supposed to affect positive separation in my airspace if I routinely cannot talk to or hear airplanes. Recommendation: The radios need [to be] fixed."