I will copy the relevant part from this answer on meta.SE: What is the cause of this sudden drop in CV queue size?
The cause was our weekly task that deletes old, abandoned questions. Unlike our daily task, which is scheduled for 3 AM UTC, the weekly task is scheduled for anytime on Saturday (actually, it's 7 days since the last run, on a Saturday, so this will cause the time to shift).
So it is very likely that the feed which posts number of unanswered question in the mentioned chat room makes the post on Saturday after the script which deletes abandoned question. The relevant messages can be found here and here. I will add that some users have wondered about this in chat, and clean-up scripts were suggested as a possible explanation. See, for example, here.
Although there are some irregularities. For example, there was decrease on June 28, which was Tuesday and we saw increase the Saturday before that. If I had to guess, maybe sometimes the script does not run as scheduled and has to be restarted manually.