Have you looked at the volume of data going in?
I saw some similar spikes for a stream managed by my company. In that case the ingress rate was very low / zero, which meant the messages were being batched - over multiple days!
Related article that got me thinking message batching might be the cause: https://repost.aws/questions/QURNKc0PceTeGIjWyWBCQa0w/why-does-lambdas-iterator-age-increase-when-using-kinesis-data-streams-enhanced-fan-out