In order for the algorithm to have stable behavior, the replay buffer should be large enough to contain a wide range of experiences, but it may not always be good to keep everything.
The larger the experience replay, the less likely you will sample correlated elements, hence the more stable the training of the NN will be. However, a large experience replay also requires a lot of memory and it willmight slow training. So, there is a trade-off between training stability (of the NN) and memory requirements.
The authors of the linked article state (right after the sentence above)
If you only use the very-most recent data, you will overfit to that and things will break; if you use too much experience, you may slow down your learning. This may take some tuning to get right.