ZAB Center Controller reported the sector's radio frequency and BUEC were out of service and made it difficult to communicate with aircraft. Reporter further stated Sector 70's frequency has been unreliable for some time.

Narrative

The aircraft was deviating for weather and advised they were back on course. They were flying towards some more moderate precipitation. I had called the weather to them when they initially checked on my sector but I did not call it to them after they continued on course.Sector 70's normal frequency of 120.95 was out of service due to an ongoing issue of feedback and squeals being heard by aircraft. The latest occurrence of this issue occurred today where several pilots said the word unsafe" on frequency in regard to the issue. Furthermore; this issue has been "tracked" for months or longer with no fix provided by the agency.Regarding this incident; I was engaged in a conversation with my Supervisor regarding the sector's normal frequency possibly being put back into service; and whether or not the frequency was actually working or if I should have an aircraft monitor said frequency to see if they heard any "popping" noises. Around this time I shipped the aircraft to the next frequency. I did not notice any buildup of precipitation in front of them beyond some scattered moderate blips at this point. A few minutes later on the next frequency; the aircraft appeared to be over heavy to extreme precipitation and was reporting extreme turbulence in a rapid descent. I don't remember if I failed to call the heavy/extreme precipitation due to being distracted by the frequency issues; or if it built quickly after I shipped the aircraft. Regardless; I was distracted by the ongoing frequency issues.Recommendation: Sector 70's frequency has been used on a wing and a prayer for months. Prior to being put out of service this morning; the BUEC's (Backup Emergency Communication) were out of service. This left us with an insufficient number of transmitters for a frequency that has had known issues for a long time. The fact that this frequency has not been repaired is a safety issue as evidenced by what happened this afternoon. The agency needs to either put the frequency out of service; combine Sector 70 with 95; and mitigate the traffic; or they need to repair the frequency for the safety of the flying public."