Someone needs to regularly call
depositBufferedEther so the deposited ether is deposited into eth2.
I made a Keep3r network job which does exactly that. The network seems to work extremely well, we had all deposits processed by keepers without even announcing a new job was live.
The job processes 8-32 (256-1024 ether) deposits at a time and pays keepers 110% of fast gas price as reported by Chainlink (the default). It stops for a day if it detects a key shortage, i.e. less deposits processed than it requested.
Production. The job is deployed at 0x1EE5C83C4B43aaEd21613D5cc7835D36078ce03F.
Its status and available credits can be seen on keep3r.network.