A TRACON Controller reported they attempted to climb an aircraft but lost communications and the aircraft flew below the Minimum Vectoring Altitude. The sector frequencies were taken out of service and the controller was not notified.

Narrative

I departed Aircraft X off of ZZZ with ZZZZZ as the next fix. I radar identified them and turned them to ZZZZZ and told them that I would climb as they made the turn due to the ZZZ1 arrivals. We were in radio communication at this point; and she took the turn. I went to climb her to 10000 ft. and she didn't respond. They were getting close to the 2500 ft. MVA so I did the low altitude alert and continued trying to get a hold of them. The Flight Data Controller came over to help as I continued to issue the low altitude alert and tried Guard to get a hold of the aircraft. I then plugged into the Orange jack after I heard the aircraft try to get a hold of me and I could not speak back to them. My handoff turned on the e frequencies and I unplugged from the orange jack and tried the e freq which is when I got them. The aircraft was at 2000 ft. in a 3800 ft. MVA. I immediately issued the low altitude alert for approximately the 4th time and climbed them. They advised me they had terrain in sight and I told them to maintain their own terrain and obstruction avoidance and continue the climb. We had a conversation about what happened and the Pilot and Co Pilot told me they tried to get a hold of me twice; which I heard both times; but they could not hear me at all. They added that if they had not gotten a hold of me when they did they would have initiated a climb on their own and had run this exact scenario in a SIM lab recently. We were told after the whole thing happened that my main and standby frequencies were posted out at that time and no one told us and it was not posted on our [form]. XXX.XX is a major frequency at Tracon and the most important in our area. The fact that we were never told it was going out and it wasn't posted is absolutely dangerous to anyone flying in the ZZZ2 area. This was an avoidable accident and I hope the reason the outage was never relayed to us is uncovered and new procedures are put in place because it can never happen again