Beacon chain lags behind frequently when running the latest `tree-states` branch

## Description

After merging in latest `unstable` to `tree-states` in PR #4514 , the BN running `tree-states` version seems to lag behind quite frequently for some reasons.

<img width="623" alt="image" src="https://github.com/sigp/lighthouse/assets/742762/f6a05319-ef6e-4b4b-9add-731af2bdb3c6">
