FSM TRACON Controller reported recurring frequency outages in the FYV sector contributed to a NMAC that occurred at a nearby airport.

Narrative

Our FYV area sector is located around 50 miles north of our facility location. As such we have telco lines that run from our facility up to three frequency banks that we use for that sector since the transmitters located at Fort Smith can't reach. We have had multiple times throughout these past two years experienced telco outages that will not only affect our direct lines to the towers in that airspace; but will cause us to lose some or all of our frequencies as well. The event in question happened on Day 0 while I was training on Radar. We were working a few VFR aircraft in our airspace when my trainee went to switch an aircraft to advisory frequency. When they keyed up I could tell that the transmission didn't sound right and I was almost sure we had lost our frequencies. When they tried a second time without response I was convinced so I had them try to reach out to a different aircraft. When they didn't respond I took over the position and started working through getting the aircraft on our emergency backup frequency. I was able to reach them on an alternative transmitter and terminated services for all the VFR aircraft we were talking to. We didn't have any IFR traffic and thankfully another Radar controller had already called ZME center and advised them they would be taking the airspace. It was a smooth transfer as soon as we were able to get them to take it and all concerned parties were notified.While occasional equipment outages are expected and part of the job to handle; the repeated and severe nature of these outages poses a threat to the safety of air traffic and the flying public.. This is highlighted by the NMAC that occurred at ZZZ airport months prior. Communication is everything in this line of work. We need a stable and reliable line of communication between us; the pilots; and the adjacent facilities. A new or upgraded line to our remote transmitter sites and between us and ZME is imperative before an NMAC becomes a collision. While ZME does a great job controlling our airspace in our absence; they are not approach controllers and do struggle when the traffic load gets to be heavy. They cannot be expected to work our airspace with anywhere close to the same sort of efficiency and are already working their normal workload as well as ours now.