DOT/DOQ Server BUG When its used for a public DNS server

### Prerequisites

- [X] I have checked the [Wiki](https://github.com/AdguardTeam/AdGuardHome/wiki) and [Discussions](https://github.com/AdguardTeam/AdGuardHome/discussions) and found no answer

- [X] I have searched other issues and found no duplicates

- [X] I want to report a bug and not ask a question

### Operating system type

Linux, OpenWrt

### CPU architecture

AMD64

### Installation

GitHub releases or script from README

### Setup

On one machine

### AdGuard Home version

0.107.19

### Description

I used ADG to build an encrypted DNS service that is widely used in my region. I directly used ADG's built-in encrypted DNS server function to provide services for everyone.

But there has always been a trouble that has troubled me for a long time, and it still occurs repeatedly in multiple version updates. After I have changed the operating environment or server many times, the problem still exists.

The specific performance is that DOT/DOQ suddenly cannot accept any analysis after working for a period of time. It needs to be restarted several times or click the "Save Configuration" button again before the analysis function can be restored. I used LSOF to query the port listening, and everything is normal.

And this problem will exist when the amount of resolution is large, such as when I use it as a public DNS resolution tool.

If it is only for personal use (means requests low), it is basically impossible to reproduce the problem.