Unresponsive REST API and bursts of logs
**Describe the bug**
Our `testing-01` node on `linux-02.ih-eu-mda1.nimbus.mainnet` is exposed public under http://testing.mainnet.beacon-api.nimbus.team/.

Recently it has been becoming unresponsive to API calls:
```
jakubgs@linux-02.ih-eu-mda1.nimbus.mainnet:~ % curl -v 0:9301/eth/v1/node/syncing
*   Trying 0.0.0.0:9301...
* connect to 0.0.0.0 port 9301 failed: Connection timed out
* Failed to connect to 0.0.0.0 port 9301 after 129641 ms: Connection timed out
* Closing connection 0
curl: (28) Failed to connect to 0.0.0.0 port 9301 after 129641 ms: Connection timed out
```
And logs behave in a weird way, where nothing is logged for 30 seconds and then a burst of logs appears.

The version is `v24.2.2-fc9c72`.

**Additional context**
Not sure releated but logs contain errors like this:
```json
{
  "lvl": "DBG",
  "ts": "2024-03-08 14:06:42.698+00:00",
  "msg": "Error occured while sending response",
  "topics": "beacnde",
  "meth": "GET",
  "peer": "78.130.168.30:43252",
  "uri": "/eth/v1/beacon/states/8200672/validators?id=25880,25881,25882,25883,25884,25885,25886,25887,25888,25889,25890,25891,25892,25893,25894,25895,25896,25897,25898",
  "reason": "Unable to send response body, reason: Stream finished or remote side dropped connection"
}
```